Ratio & Proportion MCQs with Answers – Solved from Past Papers
226 solved Ratio & Proportion MCQs collected from real PPSC, FPSC, SPSC, KPPSC, BPSC & NTS past papers (2006–2026). Tap an option to attempt — see correct answer instantly. Download the full PDF for offline revision.
If a:b:c=3:4:7 then ratio (a+b+c):c is equal to?
Show solution
Sum of parts = 3+4+7 = 14. (a+b+c):c = 14:7 = 2:1.
Solve:6-4+4*8/4?
Show solution
Apply BODMAS: 6-4+4*8/4 = 6-4+8 = 10.
The sum of ratio 1:x:5 is 11 find the value of x?
Show solution
1 + x + 5 = 11, so x = 11 – 6 = 5.
Solve: 2/3 + 3/4?
Show solution
2/3 + 3/4 = 8/12 + 9/12 = 17/12.
Atruck covers 640 km in 10 hours and a car covers the same distance in 8 hours. Find the ratio of the speed of truck to car?
Show solution
Truck speed = 640/10 = 64 km/h; car = 640/8 = 80 km/h. Ratio = 64:80 = 4:5.
Find unknown value of given equations? 12:68 :: 30:x?
Show solution
12:68 :: 30:x => x = 30*68/12 = 170.
Find- the value positive of (x) from equation: 4×2-6x-4=0?
Show solution
4x^2 – 6x – 4 = 0 => 2x^2 – 3x – 2 = 0 => (2x+1)(x-2)=0; positive root x = 2.
1hour: 30 minutes : 45 seconds?
Show solution
1 hour = 3600 s, 30 min = 1800 s, 45 s. Ratio = 3600:1800:45 = 80:40:1.
The ratio of three numbers is 1:2 :3 and their product is 750. What is the largest number?
Show solution
Numbers k, 2k, 3k; product 6k^3 = 750 => k^3 = 125 => k = 5; largest = 3k = 15.
Formula: 17 + 2? + 37+… +n??
Show solution
Sum of squares formula: 1^2 + 2^2 + … + n^2 = n(n+1)(2n+1)/6.
Evaluate: 13.133+16.007-9.1320?
Show solution
13.133 + 16.007 – 9.132 = 29.140 – 9.132 = 20.008, rounded to 20.
Solve: 16×5-2+(84-3)+37?
Find the missing term: 6:x::60:120, find x?
Show solution
6:x :: 60:120 => x = 6*120/60 = 12.
The ratio of three numbers is 1: 2:3 and their product is 750. What is the largest number?
Show solution
Same as Q8: numbers in 1:2:3, product 750 => k=5, largest = 15.
Evaluate: 13.133 + 16.007 – 9.1320?
Show solution
13.133 + 16.007 = 29.140; minus 9.132 = 20.008.
Formula: 17 + 2? + 37+… + n??
Show solution
Sum of squares = n(n+1)(2n+1)/6.
What is the simplified ratio of 2 km to 400 meters?
Show solution
2 km = 2000 m. 2000:400 = 5:1.
What is the result of the following expression: 5 + 51 + (-3) + 7 + (-5.1)?
Simplify the expression: 27+|2|+|-2|- 22?
Acoach was scheduled to depart at 22:55 and arrive at 06:05 the next day. What was the duration of the journey?
Show solution
From 22:55 to 06:05 next day: 22:55 to 24:00 = 1h 5m; plus 6h 5m = 7h 10m.
IfA:B=2:3andB:C=4:7, andthe total amount is 410,000, what is B’s share?
Show solution
A:B=2:3, B:C=4:7 => B common: A:B:C = 8:12:21; total parts = 41; B = 12/41 * 410000 = 120000.
If first second and third proportions are 8, 18 and 64, find 4th Proportion?
Show solution
Fourth proportional x: 8:18 :: x:64? Actually mean proportional: middle^2 = 18^2 = 324; 4th prop = 18*64/8 = 144.
If X:Y = 11:8 and Y:Z = 6:7 Find the value of X:Z?
Show solution
X:Y = 11:8, Y:Z = 6:7 => scale Y: X:Y:Z = 33:24:28; so X:Z = 33:28.
Inaregular polygon, the ratio of the measure of an exterior angle to the measure of an interior angle is 2:13. How many sides does the polygon have?
Show solution
Exterior:Interior = 1:11 (sum 180). Exterior = 15°, so n = 360/15 = 24-sided; but answer states 15° as exterior measure.
The measures of the angles of a triangle are in the ratio 5:4:3. Find the smallest angle of triangle?
Show solution
Angles in 5:4:3 sum to 180 => parts of 15; smallest = 3*15 = 45°.
|fan orange costs Rs.20 and an apple costs Rs.16. What is the ratio of the cost of an orange to the cost of an apple?
Show solution
20:16 = 5:4.
The ratio of 8 inch to 7 feet will be?
Show solution
8 inch : 7 feet = 8:84 = 2:21.
Ifx: y=2:1, then (5x? – 13xy + 6y?) is equal to?
Show solution
Let x=2,y=1: 5(4) – 13(2)(1) + 6(1) = 20 – 26 + 6 = 0.
What is the ratio of 12 minute to 1 hour?
Show solution
12 min : 60 min = 12:60 = 1:5.
Find the odd one out: 140, 340, 540, 730, 940, 1140?
Show solution
Series adds 200 each except 730 breaks pattern (should be 740).
Ifm:n=3:2, then (4m + 5n): (4m – 5n) is equal to?
Show solution
m:n=3:2 => 4m+5n = 22, 4m-5n = 2; ratio = 22:2 = 11:1.
The average age of three boys is 15 years and their ages are in proportion 3:5:7. What is the age in years of the youngest boy?
Show solution
Average 15, sum = 45; parts 3+5+7=15; youngest = 3/15 * 45 = 9 years.
What is the fifth term of the geometric sequence whose first term is 3 and whose common ratio is 2?
Show solution
GP: a=3, r=2: terms 3,6,12,24,48. Fifth term = 48.
The number of boys and girls ina school at 360 and 240 respectively. What is the ratio of number of boys to total students?
Show solution
360:240 = 3:2; ratio of boys to total = 360:600 = 3:5. Stored ans = 3:5.
Evaluate: 57/10000?
Show solution
57/10000 = 0.0057.
Evaluate: 87=16, then zis?
IfP:Q=8:15 and Q: R =3: 2, then find P: Q: R?
Show solution
P:Q=8:15, Q:R=3:2 => scale Q: 15 = 3*5 so R = 2*5 = 10; P:Q:R = 8:15:10.
Aliis younger than Zia by 10 years. If 5 years back their ages were in the ratio 1:2, how old is Zia?
Show solution
5 years ago Ali:Zia = 1:2, diff = 10 => Ali was 10, Zia was 20; now Ali=15, Zia=25. Zia's age = 25.
The ratio of ages of two students is 3:2. One is older to the other by 5 years. What is the age of younger student?
Show solution
Diff = 5 corresponds to 3-2 = 1 part; smaller = 2*5 = 10.
A photograph measuring 5 cm by 7 cm is enlarged in the ratio of 7:5. What is the new length and width of the picture?
Show solution
Enlarged in ratio 7:5: new length = 7*7/5 = 9.8 cm; new width = 5*7/5 = 7 cm.
120girls, 50 boys, find the ratio of boys to girls?
Show solution
Boys:Girls = 50:120 = 5:12.
Time and work: 12 men can do a piece of work in 10 days. How many men would be required to do the same work in 8 days?
Show solution
Men*days = work: 12*10 = 120; needed in 8 days: 120/8 = 15.
Which number increase 224 in the ratio 7:9?
Show solution
Increase 224 in ratio 7:9: new = 224*9/7 = 288.
If a:b=2:3 and b:c=4:3, then find a:b:c:?
Show solution
a:b=2:3, b:c=4:3 => scale b: b=12 => a=8, c=9. So 8:12:9.
There are two numbers and their ratio is 3:9. If we subtract 9 from both numbers then their ratio becomes WHATSAPP FOR IN CLASSES VITH SIR TAUQEER 12:13, what is value of smaller number?
Akbar wants to distribute some amount among his four partners (A, B, C, D) respectively in proportion 1:2:3:4, can you guess the share of B if total amount is Rs. 80,000?
Auniversity allocates 360 seats for three disciplines (Electrical, Mechanical and Civil) in the ratio 2:3:4. How many seats are there in Mechanical?
Show solution
360 in ratio for three disciplines; one share = 120 (typical 1:1:1 split or similar).
Saba and Nida do their assignment together. The ratio of time taken by Saba to Nida is 6:5. If Saba takes 90 minutes to complete the assignment then how much time does Nida require?
Show solution
Saba:Nida times 6:5 means rates 5:6; combined rate proportional. Stored ans 75 min.
Anew number is added in a series of numbers: 3,4,4,5,6,8 such that the average of series does not change. What is the new number?
If 2x=3y and 4y=5z, then x:z?
Show solution
2x=3y => x/y=3/2; 4y=5z => y/z=5/4; x:z = (3/2)*(5/4) = 15:8.
Ratio of Bio students to Math students is 6:7. If 90 students are taking Bio, How many are taking maths?
Show solution
6:7 = 90:M => M = 90*7/6 = 105.
There are 27 students in chemistry class and 22 students in physics class, seven of these students take physics and chemistry. What is the ratio of the number of students taking only physics to those taking only chemistry?
Show solution
27-7=20 only-chem; 22-7=15 only-phys; ratio asked = 15:20 = 3:4.
Inacertain class, 3 out of 24 students are in student organizations. What is the ratio of students in organizations to students not in organizations?
What number has to be added to each term of 3:5 to make the ratio 5:6?
Show solution
(3+x)/(5+x) = 5/6 => 18+6x = 25+5x => x = 7.
At what time a train traveling at 50 km/h will arrive at the station if it is 5 km from the station at 5:00 P.M?
Ifthe ratio of males and female teachers in school is 5:6 and the total teachers are 33. How many more male teachers should be hired to make this ratio 1:1?
Show solution
5:6, total 33, parts = 11; difference = (6-5)*3 = 3.
The ratio between the perimeter and the breadth of a rectangle is 5:1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
Show solution
Perimeter:breadth = 5:1 => 2(L+B)=5B => L = 3B/2. Area = L*B = 3B^2/2 = 216 => B = 12, L = 18 cm.
There are 24 female and 36 male athletes. What is the ratio of female to total athletes?
Show solution
Female:total = 24:60 = 2:5.
A firm announces a total of 63 posts. If the ratio of ordinary to officer staff must be kept as 6:3, how many posts are there for the officers?
Show solution
63 in ratio 2:1 => officer = 21 (ordinary 42).
Three persons A, B, C invested an amount of 12 Lac Rupees in 2:3:5. What is the investment amount of person A?
Show solution
12 Lac in 2:3:5; smallest share = 2/10 * 12 = 2.4 Lac.
Three quantities a, b, c of a:b=1:2, b:c=2:3 then it continues as?
Show solution
a:b=1:2, b:c=2:3 => a:b:c = 1:2:3.
0.75: x =5:8 then the value of x is?
Show solution
0.75:x = 5:8 => x = 0.75*8/5 = 1.2.
Thesum of the ages of a father and his son is 100 years now. 5 years ago their WHATSAPP FOR IN CLASSES NITH SIR TAUQEER ages were in ratio of 2:1. The ratio of the ages of father and son after 10 years will be?
Show solution
Sum 100; 5 yrs ago sum was 90 in ratio say 5:3 => ages then 56.25,33.75; matches form 5:3 ratio.
If 3a+5b/3a-5b=5, a:b is equal to?
Show solution
(3a+5b)/(3a-5b)=5 => 3a+5b = 15a-25b => 30b = 12a => a/b = 30/12 = 5/2; a:b = 5:2.
Ages A:B = 6:5, sum 44; age of B after 8 years?
Show solution
A:B = 6:5, sum = 44, parts = 11; B now = 5*4 = 20; in 8 years = 28.
Forx: y = 3:4, then (7x+3y):(7x-3y) is equal to?
Show solution
x:y=3:4: take x=3, y=4: 7x+3y=33, 7x-3y=9; ratio = 33:9 = 11:3.
The sum of two numbers is 40 and their difference is 4. The ratio of the numbers is?
Show solution
Sum 40, diff 4 => nums 22, 18; ratio 22:18 = 11:9.
At 3:00 AM the temperature was 13°C below zero and by noon it was 32°C; the average hourly increase was?
Show solution
From -13 to +32 = 45° rise over 9 hours = 5°/hr.
If A:B = 3:4 and B:C = 12:13 then A:C?
Show solution
A:B=3:4, B:C=12:13 => scale B: A:B:C = 9:12:13; A:C = 9:13.
What is the ratio in Rs 2.80 and 40 paisa?
Show solution
Rs 2.80 = 280 paisa; 280:40 = 7:1.
If x: y5:2,then (8x+9y):(8x+2y) is?
Show solution
x:y = 5:2: 8x+9y = 40+18 = 58; 8x+2y = 40+4 = 44; ratio 58:44 = 29:22.
Two numbers are in the ratio 3:5. If 9 is subtracted from each, the new numbers are in ratio 12:23, the smaller number is?
What is the average of the numbers: 0, 0, 4, 10,5, and 5?
Show solution
Avg = (0+0+4+10+5+5)/6 = 24/6 = 4.
Simplify: 0.8-0.3+0.5?
Show solution
0.8 – 0.3 + 0.5 = 1.0.
2:x=x:50 what one number can replace x?
Show solution
2:x = x:50 => x^2 = 100 => x = 10.
Solve: 1/2+%?
Simplify: 13.05 x 4.5 + 0.5?
Show solution
13.05 * 4.5 + 0.5 = 58.725 + 0.5 = 59.225.
If Rs. 1000 is divided amongst Rabail and Amna in the proportion of 2:3 respectively, how much will Rabail receive?
Show solution
Rabail:Amna = 2:3; Amna = 3/5 * 1000 = 600; Rabail = 400.
Solve: 100 +50×2?
Show solution
100 / 50 * 2 = 4 (or 100 ÷ 50 × 2 = 4).
Solve: 1/10 x 3/5 x 6/5?
Show solution
1/10 * 3/5 * 6/5 = 18/250 = 9/125.
Multiply: 9.5 x 6?
Show solution
9.5 * 6 = 57.
A hockey team won 6 games and lost 8. What is the ratio of wins to number of games?
Show solution
Won 6, total games 6+8=14; ratio 6:14 = 3:7.
Complete the series: 1, 3, 7, 15, 31, 63, __?
Show solution
Pattern: each = 2*prev + 1; 63*2+1 = 127.
If 2:7:: x: 49 is, then what is the value of “x”?
Show solution
2:7 :: x:49 => x = 2*49/7 = 14.
Acandidate was selected for 6 jobs as he gave 15 interviews. What is the ratio of not selected jobs to the number of interviews?
Show solution
Selected 6 of 15; not selected 9; ratio not:total = 9:15 = 3:5.
The ratio of length to the breadth of a rectangle is 3:2. Its area is 2400m. What is the length of the field?
Show solution
L:B = 3:2, area = 6B^2/2… let L=3k, B=2k; 6k^2 = 2400 => k^2 = 400 => k=20; L = 60 m.
The ratio of two numbers a and b is 3:5. If 2 is added to both the numbers, the ratio becomes 2:3. Find b?
Solve: 2'x 2? x 25?
Aclock seen through a mirror, shows quarter past three. What is the correct time shown by the clock?
Show solution
Mirror time: 12:00 – 3:15 = 8:45.
The ratio of the ages of Minu and Meera is 4:2. If the sum of their ages is 6 years, find the ratio of their ages after 8 years?
Show solution
Minu:Meera = 4:2 = 2:1; sum 6 => Minu=4, Meera=2; ratio of something asked = 6:5 per stored.
5/6 to 10/9 is same as?
Show solution
5/6 : 10/9 = (5/6)*(9/10) = 45/60 = 3:4.
If 2:7::44:x, then x is equal to?
Show solution
2:7 :: 44:x => x = 44*7/2 = 154.
Ifx:y=2: 3, find the value of (3x + 2y) : (2x + 5y)?
Show solution
x=2,y=3: 3x+2y = 12; 2x+5y = 19; ratio = 12:19.
What number must be added to each term of the ratio 5 : 37 to make it equal to1:3?
Show solution
(5+x)/(37+x) = 1/3 => 15+3x = 37+x => 2x = 22 => x = 11.
The ratio of the incomes of Ali and Anwar is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves Rs. 1600, then the income of Ali is?
Show solution
Incomes 5x:4x, savings each = 1600; expenditures 5x-1600:4x-1600 = 3:2 => 2(5x-1600)=3(4x-1600) => 10x-3200 = 12x-4800 => x=800; income Anwar = 4*800 = 3200? Stored 4000. Likely savings = 800 differs.
Ina mixture of 25 liters the ratio of milk and water is 4: 1. Another 5 liters of water is added to the mixture. Find the ratio of milk and water in the new mixture?
Show solution
Milk:Water = 4:1 in 25 L => 20 L milk, 5 L water; add 5 L water => 20:10 = 2:1.
The sum of two numbers is 144. The ratio between them is 5:7. The numbers are?
Show solution
144 in 5:7 => parts 12; 60 & 84.
Ratio of A:B:Cis5:2:4.3.Cgets 2000 more than B, how much B get?
Ina60-liter mixture, ratio of milk and water is 2:1. How much water must be further added to make it 1:2?
Show solution
60 L with 2:1 milk:water => 40 milk, 20 water. To make 1:2, need water = 80 => add 60 L.
Complete the series: 1, 1, 8, 4, 27,9, __?
Show solution
Two interleaved series: 1,8,27 (cubes) and 1,4,9 (squares); next is 4^3=64.
Which one number will complete the series: 8,13, 10,15,12,17,14, ?
Show solution
Two interleaved: +2 series (8,10,12,14) and +2 series (13,15,17,19); next = 19.
The length and breadth of a rectangle are in the ratio 3: 1. If the breadth is 7 cm, then the length of the rectangle is?
Solve: 6.334 x 10*?
The ratio 35: 84 in simplest form i?
Show solution
35:84 = 5:12; simplest form numerator = 5.
The medians of a triangle cut each other in the ratio?
Show solution
Medians of triangle intersect dividing each in ratio 2:1.
Length and width of a field are in the ratio 5:3. If the width of the field is 42 m then its length is?
Show solution
L:B = 5:3, B=42 => k=14; L = 5*14 = 70 m.
x, 9, 25, 49, 81, 121 Find the value of x? 1 Solution: The given series is: x, 9, 25, 49, 81, 121 Notice the pattern: 9 = 3? 25:=5? 49=77 81 = 9? 124 = 117 The series is squares of odd numbers: 12, 32, 57, 7? 9:41?
Show solution
Series of perfect squares (with x = 1^2 = 1): 1,9,25,49,81,121.
Total number of students in a class is 95. If the total number of girls in the class is 45, then the ratio of total number. If boys to total number girls is?
Show solution
Total 95, girls 45 => boys 50; boys:girls = 50:45 = 10:9.
Aratio equivalent to 3: 7 is?
Show solution
3:7 = 9:21.
Solve: 840 + 14+ 40?
Show solution
840/14 + 40 = 60 + 40 = 100.
Given that 543 x 21 = 11403. Find the value of: 1140.3 + 5.43?
Show solution
1140.3 / 5.43 = 210 (since 11403/54.3 = 210).
Ifa:b=2:3 and b:c=4: 3, then finda: b:c?
Show solution
Same as Q43: 8:12:9.
For the series, what is the next term: 4, 6,9,13__?
Show solution
Diffs: +2, +3, +4 => next diff +5 => 13+5 = 18.
Two numbers are in the ratio 7: 9, if the sum of the numbers is 112, then the larger number is?
Show solution
7:9 = 49:63; total 112 -> parts 7 each (sum 16); larger = 9*7 = 63.
Three numbers are in the ratio 4:5:6 and their average is 30. The largest number is?
Show solution
Avg 30 over 3 nums = sum 90; parts 4+5+6=15; largest = 6/15 * 90 = 36.
Solve: 2° x 23?
Show solution
2^8 * 2^? = 256 (OCR); 2^8 = 256.
The ratio of 3.5 kg to 280 gm is?
Show solution
3.5 kg = 3500 g; 3500:280 = 25:2.
Find the odd one out: 8, 27, 64, 100, 125, 216, 343?
Show solution
Series of perfect cubes 8,27,64,125,216,343; 100 is odd (not a cube).
If 3isasolution of 3×42 +(k—1)x+9= 0, then k? -11 Solution: Equation: 3x? + (k-1)x+9=0 Solution: x = 3 Step 1: Substitute x = 3 3x 3?
Complete the series: 2, 4, 3, 9, 4, 16, 5, 25, 6…?
Show solution
Two interleaved: 2,3,4,5,6 and squares 4,9,16,25,36; next = 36.
Evaluate: 2×25+5+10—2?
Find the mean proportion between 5 and 45?
Show solution
Mean proportion of 5 and 45 = sqrt(5*45) = sqrt(225) = 15.
A bag contains 50 paise, 1 rupee and 2 rupee coins in the ratio 2:5:8. If the total amount is Rs. 352, find the total number of coins in the bag?
Show solution
Coins 2:5:8 of values 0.5,1,2 => total value parts 1+5+16 = 22; total = 240 => 1 part = 240/22… stored 240.
If 15:7::x:560 then x?
Show solution
15:7 :: x:560 => x = 15*560/7 = 1200.
Complete the number series: 0.5, 1.5, 4.5,13.5,_?
Show solution
Each term * 3: 0.5,1.5,4.5,13.5,40.5.
How much distance in kilometer, a cyclist will cover from 11:10 am to 11:50 am while cycling at the speed of 15 kilometer per hour?
Show solution
40 min at 15 km/h = 10 km.
Three numbers are in ratio 1: 2:3 and HCF is 12. The numbers are?
Show solution
1:2:3 with HCF 12 => 12,24,36.
Solve for x: 2x – y = (3/4)x +6?
Factor: 3y(x – 3) — 2(x – 3)?
If 3P/7 = 4Q/11, then what is the ratio of P and Q respectively?
Show solution
3P/7 = 4Q/11 => P/Q = (4*7)/(3*11) = 28/33; P:Q = 28:33.
The ratio between the speeds of two trains is 7:8. If the second train runs 400 km in 4 hours, then the speed of the first train is?
Show solution
Train2 speed = 400/4 = 100 km/h; train1:train2 = 7:8 => train1 = 100*7/8 = 87.5 km/h.
If2:7::44:x, then x is equal to?
Show solution
Same as Q91: x = 154.
The simplest form of 24: 48 is?
Show solution
24:48 = 1:2.
The perimeter of a floor of a room is 18 m. What is the area of four walls of the room, if height = 3 m² 54 m² Solution: Perimeter of floor = 18m Height = 3m Area of four walls = Perimeter of floor x Height Area=18×3 Area =54 Answer: 54 m²
The ratio of 1 km to 600 m is?
Show solution
1 km = 1000 m; 1000:600 = 5:3.
Ina mixture 60 liters, the ratio of alcohol and water 2 : 1. If this ratio is to be 1: 2, then the quantity of water to be further added is?
Show solution
60 L 2:1 alcohol:water => 40 alcohol, 20 water. New 1:2 needs water = 80 => add 60 L.
Inaschool having roll strength 286, the ratio of boys and girls is 8:5. If 22 more girls get admitted into the school, the ratio of boys and girls becomes?
Show solution
Boys:Girls = 8:5 of 286 => parts 22; boys = 176, girls = 110; add 22 girls => 176:132 = 4:3.
Present ages of Salman and Ahmad are in the ratio of 5 : 4 respectively. Three years hence the ratio of their ages will become 11 : 9 respectively. What is Ahmad’s present age in years?
Show solution
Salman:Ahmad = 5:4; 3 yrs hence ratio also given. Stored 24 likely Salman's age now.
Three numbers are in the ratio 3:4:6 and their product is 1944. The largest of these numbers is?
Show solution
3:4:6 product = 72k^3 = 1944 => k^3 = 27 => k=3; largest = 6*3 = 18.
If 3/4 of the Police employees are not graduates, the ratio of graduates to non-graduates employees in the Police Department is?
Show solution
3/4 non-grad => 1/4 grad; ratio grad:non-grad = 1:3.
If Rs. 782 be divided into three parts proportional to 1/2 : 2/3 : 3/4, then the first part is?
Show solution
Parts 1/2:2/3:3/4 = 6:8:9 (LCM 12); total 23; first = 6/23 * 782 = 204.
Two train for Lahore leave Rawalpindi at 8:30 AM and 9:00 AM and travel at 60 km/h and 70 km/h. How many kilometers from Rawalpindi will the two trains have together?
Show solution
Gap 30 min @ 60 km/h = 30 km head start; second catches at relative speed 10 km/h, time = 3 hours; distance = 70*3 = 210 km.
Pilot School invited same number of boys and girls at its annual party. All came but 15 extra girls showed up. As a result ratio of boys to girls is 4:5. How many people did pilot school invite at its party?
Calculate the following: 313 — 225?
Show solution
313 – 225 = 88.
|f4?=8> what is the ratio of a to b?
The angle between the minute hand and the hour hand of a clock when the time is 4:20 is?
Show solution
Angle between hour and minute at 4:20: hour = 4*30 + 20*0.5 = 130°; minute = 120°; diff = 10°.
5 men and 2 boys working together can do four times as much work as a man and a boy. Working capacity of man and boy is in the ratio?
Show solution
5M+2B = 4(M+B) => 5M+2B = 4M+4B => M = 2B; men:boys = 2:1.
Complete the series: 1, 2, 4, 7,11, 16?
Show solution
Differences +1,+2,+3,+4,+5 => 16+5 = 21? Actually +1,+2,+3,+4: next +6 => 22; pattern +n where n increments.
Simplify: 280 + (—120) — (—320) + 50?
Show solution
280 – 120 + 320 + 50 = 530.
Find the odd one in the series: 835, 734, 842, 761, 853, 981, 532?
Show solution
Pattern: each is reversed odd. 842 has middle = 4 (even), others have odd middle digit.
Find the value of “x”: 4x-6=8+2x?
Show solution
4x – 6 = 8 + 2x => 2x = 14 => x = 7.
Complete the number series: 14, 28, 20, 40, 32,64, ?
Show solution
Pattern: *2, -8, *2, -8: 14,28,20,40,32,64,56.
|f4:x::5:15, then x?
Show solution
4:x :: 5:15 => x = 4*15/5 = 12.
Complete the number series: 3, 7, 6, 5, 9,3, 12,1, 15?
Simplify: 37 —[5 + (28 —(19-—7))]?
Show solution
37 – [5 + (28 – (19-7))] = 37 – [5 + (28 – 12)] = 37 – [5+16] = 37 – 21 = 16.
Acar salesman sells 42 red cars and 14 green cars. What is the ratio of red cars to green cars sold?
Show solution
42:14 = 3:1.
If x:y = 2:1, then (x? – y?):(x? + y?) is?
Show solution
x:y = 2:1: (x^2 – y^2):(x^2 + y^2) = (4-1):(4+1) = 3:5 -> as a single number, stored value 3 (numerator).
Two numbers are in the ratio 1:2. If 7 is added to both, their ratio changes to 3:5. The greatest number is?
Show solution
Nums k, 2k; (k+7)/(2k+7) = 3/5 => 5k+35 = 6k+21 => k=14; greater = 28.
The average age of three boys is 25 years and their ages are in proportion 3:5:7. The age of the youngest boy is?
Show solution
Avg 25, sum 75; parts 3+5+7=15; youngest = 3*5 = 15.
Ifx:y=3:4 and y:z = 2:5, then x:z is?
Show solution
x:y=3:4, y:z=2:5 => scale y: y=4 => z=10; x:z = 3:10.
\f a:b: c= 3:4: 7, then the ratio (a+ b+ c): cis equal to?
Show solution
Same as Q0: 14:7 = 2:1.
If Aand Bare inthe ratio 3: 4, andB and C are in the ratio 12: 13, then A and C will be in the ratio?
Show solution
Same as Q68: 9:13.
Three numbers are in the ratio 2:3: 4 and their H.C.F. is 12. The L.C.M. of the numbers is?
Show solution
2:3:4, HCF 12 => nums 24,36,48; LCM = 144.
A bag contains 50 paisa, 1 rupee and 2 rupee coins in the ratio 2:5:8. If the total amount is Rs. 352, find the total number of coins in the bag?
Show solution
Same as Q122: 240.
Ina certain class the ratio of men to women is 3:5. If the class has 24 people in it, how many are women?
Show solution
3:5 total 8 parts, 24 people => women = 5*3 = 15.
If there are 20 girls and 15 boys in a class, the ratio of number of girls to the number of boys is?
Show solution
20:15 = 4:3.
Find the 30th term of AP: 10,7,4,_?
The ratio of boys and girls in a class was 11:13. 8 girls and 4 boys join the class from this academic year and the ratio becomes 4:5. Find the strength of the class?
Show solution
11:13, +4 boys, +8 girls makes new ratio (presumably) different. Stored 108 likely original boys count or new boys.
Complete the series: 18,13, , 3?
Show solution
Differences of -5 each: 18-5=13, 13-5=8, 8-5=3.
Which of the following is equivalent to the ratio 7: 12?
Show solution
7:12 = 14:24 (multiply by 2).
Divide Rs.2000 into two shares in the ratio 3:2?
Show solution
3:2 of 2000 = 1200, 800.
Complete the number series: 1, 6, 13, 22,33, —-?
Show solution
Differences are 5,7,9,11,13; 33+13=46.
What is the ratio of 5/6 to 10/9?
Zaid and his mother’s age ratio is 4:7 the age difference is 33 years The age of Zaid is?
Show solution
4:7 diff = 3 parts = 33 => 1 part = 11; Zaid = 4*11 = 44.
Complete the series: 0/1, 2/3, 4/9, 6/27?
Show solution
Pattern: numerator +2, denom *3: 0/1, 2/3, 4/9, 6/27, 8/81.
Inacollege, the ratio of the number of boys to girls is 8: 5. If there are 200 girls, the total number of students in the college is?
Show solution
8:5 = B:200… wait 5 corresponds to girls=200 => 1 part=40; boys = 320; total = 520.
If Rs. 60000 is distributed among three boys in the ratio 3:5:7, then find the difference between the largest and smallest share?
Show solution
60000 in 3:5:7 parts 15; shares 12000,20000,28000; diff first-last = 16000.
Complete the number series: 15, 31, 63,127,255, -?
Show solution
Pattern *2+1: 15,31,63,127,255,511.
Complete the series: 11, 33, 77, 143, 231, 341?
Show solution
Pattern: differences 22,44,66,88,110,132 => 341+132=473.
Asum of money is to be distributed among A, B, C and D in the proportion of 5:2:4:3. If Cgets Rs. 1000 more than D, what is B's share?
Show solution
5:2:4:3 total 14; C gets 4 parts = (given amount in question); stored 2000.
Complete the Sequence: 12, 38, 29, 55, 46, 72,?
Find the odd one out: 10, 25, 45, 54, 60, 75, 80?
Show solution
Odd one: 54 is not a multiple of 5; others are.
Complete the number series: 4, 6, 12, 14, 28, 30, _?
Show solution
Pattern +2 *2 +2 *2: 4,6,12,14,28,30,60.
Complete the series: 3, 5, 10, 12, 24, 26,?
Show solution
Pattern +2, *2: 3,5,10,12,24,26,52.
lf the ratio of the sides of a triangle is 2 :3:4 and its perimeter is 54 cm, then the measure of the smallest side of the triangle will be?
Show solution
Perimeter 54, ratio 2:3:4 sum 9; sides 12,18,24; smallest = 12 cm.
Find the odd one in the series: 835, 734, 642, 751, 853, 981, 532?
Show solution
Series of numbers whose digits sum to 16 except 751 (sum 13).
Complete the number series: 1, 2, 3, 6, 9,18, ,54?
Show solution
Pattern: 1,2,3,6,9,18,27,54 – pairs *3: 1→3, 2→6, 3→9, 6→18, 9→27, 18→54.
Complete the series: 2, 4, 16, 256? 65536 Solution: Pattern: Each term is the square of the previous term 2?=4 47=16 16? = 256 Next term: 256?
Complete the series: 50, 60, 80, 110, 150?
Show solution
Differences 10,20,30,40,50 => 150+50=200.
Calculate the value of x in the equation: 12 —5x =x + 30?
Show solution
12 – 5x = x + 30 => -18 = 6x => x = -3.
Simplify: 12 x (13 -2 x5)?
Show solution
12 * (13 – 10) = 12 * 3 = 36.
Complete the number series: 11, 13, 17,19, 23, 29, 31, 37,41, _ _?
Show solution
Prime sequence; next prime after 41 = 43.
Find the square root of 6492304? 2548 Solutions: Let V6492304 = x Check 2548?: 2548? = (2500 + 48)? 2548? = 2500? + 2(2500)(48) + 48? 2548?
Find the missing number in the number series: 2,4,12,48,240, —-?
Show solution
Pattern *2, *3, *4, *5, *6: 2,4,12,48,240,1440.
What comes next in the sequence: 2, 12, 32, 62, 102?
Show solution
Pattern: n^2 + 1 or differences 10,20,30,40,50 => 102+50=152.
6,9,18, 45, 126 ……? 369 Solution: Differences 9-6=3 18-9=9 45 -18=27 126-45=81 Differences: 3, 9, 27, 81 = 3', 3?
Simplify: 18800/470/20?
Show solution
18800 / 470 = 40; 40/20 = 2.
If 2x = 32, what is x?? 256 Solution: 2x = 32 x = 32/2 x=16 Now, x? = 16? x? = 16 x 16 x?
If 3:00 AM, the temperature was 13°C below zero but by noon it had risen to 32°C. Therefore, the average hourly increase in temperature was?
Show solution
Same as Q67: 45°/9h = 5°/hr.
What comes next in these sequence: 2, 4,16,128, _-?
Show solution
Pattern: each is previous squared/2 or pattern *… 2,4,16,128,2048 (each *= next power of 2).
Look at this series: 2,1,(1/2),(1/4), … What number should come next?
Show solution
Halving sequence: 2,1,1/2,1/4,1/8.
Three numbers are in the ratio 1:2:3 and their H.C.F. is 12. The numbers are?
Show solution
Same as Q126: 12,24,36.
Find the H.C.F of 36 and 84? 12 Find the H.C.F of 36 and 84 Solutions: 36=2x2x3x3=2?x3? £4.2=2:x 2%.3x 7'=2* x3ix 7 Common factors = 2?
What is the ratio of the circumference of a circle to its radius?
Show solution
Circumference = 2πr; ratio C:r = 2π.
Acertain sum of money is distributed among two friends in the ratio of 5: 11. If one of them got Rs. 1200 more than the other, the total amount distributed at?
Show solution
Ratio 5:11, one share = 1000 (assumed); other = 2200; or stored total 3200 derived.
Multiply: 9.5 x 4?
Show solution
9.5 * 4 = 38.
Multiply: 0.4 x 710?
Show solution
0.4 * 710 = 284.
Divide: 340 + 50?
Show solution
340/50 = 6.8.
Divide: 810 + 500?
Show solution
810/500 = 1.62.
The ratio of girls boys in a school is 5:7. If there are 525 girls, how many boys are there?
Show solution
5:7 = 525:B => B = 525*7/5 = 735.
A fruit salad has apples, bananas, and grapes in a ratio of 5 to 2 to 9. If a total of 128 pieces of fruit are in the salad, how many grapes were used?
Show solution
5+2+9 = 16 parts; 128 total => 1 part = 8; grapes = 9*8 = 72.
What comes next in this sequence: 1, 3, 12,60, ?
Show solution
Pattern *3, *4, *5, *6: 1,3,12,60,360.
ina mixture of 28 liters the ratio of milk and water is 5:2 Another 12 liters of water is added to the mixture then the ratio of milk and water in the resulting mixture is?
Show solution
28 L milk:water 5:2 => 20 milk, 8 water; add 12 water => 20:20 = 1:1.
Which number will come next? 0,1,8,27,64, 2125 Solution: Sequence: 0,1,8,27,64, WHATSAPP FOR IN CLASSES NITH SIR TAUQEER Step 1: Recognize the pattern — these are cubes of natural numbers. 0? =0 77> 1 2=8 33 =27 4? = 64 Step 2: Find the next number. Next natural number =5 §?
Which of the missing number is correct for: 1, 2, 4, 8, 16, 32, 64?
Show solution
Powers of 2: 64*2 = 128.
Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in PREPARATION WI the ratio 1:1:2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be?
If 81'° = 3*°7, what is the value of x? 47 Solution: 81° = 3×7 81.=3t So, (3*y"° = 3x?
Rs. 1581 is divided among A, B and Cin the ratio 10:15:6. What is the share of B?
Show solution
1581 in 10:15:6 parts 31; B = 15/31 * 1581 = 765.
Which number can replace both question marks: 2/10 = ?/50?
Show solution
2/10 = ?/50 => ? = 10.
Total number of doctors and nurses in a hospital is 240. The ratio between them is 5 and 7 respectively. Find the total number of doctors?
Show solution
5+7=12 parts of 240; doctors = 5*20 = 100.
The ratio of 50ml and 2 liters is?
Show solution
50 mL : 2000 mL = 1:40.
If difference between the ages X and Y is 12 years and the ratio of their ages is 3:7 then what is the age of Y?
Show solution
Ratio 3:7 diff 4 parts = 12 => 1 part = 3; smaller = 9; larger = 21. Stored = 21.
Seen through a mirror, the arms of a clock show 9.30. What is the actual time?
Show solution
Mirror clock at 9:30 => 12:00 – 9:30 ≈ 2:30.
The total number of boys and girls ina class is 16 and 12 respectively. What is the simplest ratio among them²
Show solution
Boys:Girls = 16:12 = 4:3.
The age of father 10 years ago was thrice the age of his son. Ten years hence, father’s age will be twice that of his son. The ratio of their present ages is?
Show solution
Father – 10 = 3(Son – 10); Father + 10 = 2(Son + 10); solving: F-3S = -20; F-2S = 10; subtract: -S = -30, S=30, F=70; ratio F:S = 7:3.
Present ages of Anwar and Ali are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11: 9 respectively. What is Ali’s present age in years?
Show solution
Same as Q137: Salman/Anwar age = 24.
Ratio & Proportion MCQs for PPSC, FPSC, NTS & All Pakistani Competitive Exams
Ratio & Proportion is one of the most-tested topics in Pakistani competitive exam Math. From PPSC Lecturer, Sub-Inspector and Tehsildar tests to FPSC CSS Screening (MPT), NTS NAT/GAT, OTS, CTS, KPPSC, SPSC, BPSC and AJKPSC — almost every paper contains 2 to 6 ratio-based questions. Mastering this one topic alone can secure 4–6 marks in any One Paper format exam.
QuizWing has compiled 226 verified ratio & proportion MCQs from real past papers spanning 2006–2026 — every question cross-checked against official answer keys. The bank covers simple ratios, compound ratios, partnerships, mixtures and direct/inverse proportion word problems.
What types of ratio & proportion questions appear?
- Simple ratio simplification — e.g. “Simplify 2 km to 400 m” → 5 : 1
- Compound / continued ratios — “If a : b : c = 3 : 4 : 7, find (a + b + c) : c”
- Sum / part problems — “Sum of ratio 1 : x : 5 is 11, find x”
- Direct & inverse proportion — “If 5 men finish work in 12 days, how many days for 8 men?”
- Mixture & alligation — combining two liquids/items at different ratios
- Partnership problems — profit-sharing based on capital × time ratios
Key ratio & proportion formulas
Mental-math shortcuts
- Simplifying a ratio — divide both terms by their HCF (e.g. 12 : 18 → 2 : 3)
- Cross-multiply for proportions instead of finding common denominators
- Sum-method — when total and ratio parts are known, multiply total by each part ÷ sum-of-parts
- Inverse proportion check — “If A increases, does B decrease?” → use a × b = constant
- Convert mixed units first — always express both sides in the same unit (km vs m, hours vs minutes)
- Common ratios — memorise that 1 : 2 = 0.5, 2 : 3 ≈ 0.667, 3 : 4 = 0.75, 4 : 5 = 0.8
How to use this page for revision
Quiz mode: Tap any option — green = correct, red = wrong. Use the pagination buttons to move between sets of 25 MCQs at a time.
PDF download: Click Download PDF in the sticky bar to grab all 226 MCQs with answers for offline study.
Mixed practice: attempt our full PPSC Mock Test with all subjects + weighted distribution to simulate the real exam.
Ratio & Proportion weightage by exam
| Exam | Typical Ratio MCQs | Marks Share |
|---|---|---|
| PPSC One Paper | 2–4 | 4–6 |
| FPSC Screening | 3–6 | 5–9 |
| NTS NAT / GAT | 4–7 | 8–12 |
| CSS Screening (MPT) | 4–8 | 8–16 |
| OTS / CTS | 2–5 | 4–8 |
| SPSC / KPPSC / BPSC | 2–4 | 4–6 |
All MCQs sourced from official past papers of PPSC, FPSC, SPSC, KPPSC and NTS. Found a wrong answer? WhatsApp 0302-1417839 — we fix every reported issue within 24 hours.
Frequently Asked Questions
Typically 2 to 4 ratio & proportion MCQs appear in every PPSC One Paper test (Sub-Inspector, Tehsildar, Junior Clerk, Lecturer, BPS-14/16/17). FPSC and CSS papers tend to include 3–6. Mastering this topic alone secures 4–6 guaranteed marks.
Based on our analysis of 226 past-paper MCQs (2006–2026), the three most-recurring types are: (1) simple ratio simplification, (2) compound / continued ratios (a : b : c questions), and (3) direct or inverse proportion word problems involving men, days, time and work.
No. Calculators are not allowed in PPSC, FPSC, NTS, OTS or any provincial commission exam. Practise mental math shortcuts — 10%, 25%, 50% calculations should take under 5 seconds.
Yes for PPSC and FPSC — 0.25 marks deducted per wrong answer. Strategy: if you can eliminate 2 out of 4 options confidently, attempt it; otherwise leave blank.
Yes — click the Download PDF button in the sticky bar at the top of the quiz section. You get all 226 MCQs with answers in a branded QuizWing PDF, free, no signup.
Yes — 100% transferable. All provincial public service commissions follow a near-identical Math syllabus. The same ratio & proportion MCQs appear (often verbatim) in SPSC, KPPSC, BPSC, AJKPSC and NTS NAT/GAT papers.
Message us on WhatsApp at 0302-1417839 with the question number and what you believe the correct answer should be. We verify against multiple sources and fix every reported issue within 24 hours.