PPSC Mathematics Past Paper 2018 Solved MCQs with Answers
Solved Mathematics MCQs from the PPSC 2018 past paper, each with the correct answer and a clear explanation. Ideal practice for PPSC, FPSC, NTS, CSS and PMS. All questions are extracted from the actual 2018 paper and verified before publication.
After adding 1.5 and 2.5 the result will be?
1.5 + 2.5 = 4.
24375 books are to be arranged equally in shelves. If 375 books are arranged in each shelf, how many shelves will be needed?
24,375 / 375 = 65 shelves.
Simplify using BODMAS rule 5 x 3 – 4 x 2 + 1?
Under BODMAS, multiplication comes first: 15 – 8 + 1 = 8.
HCF of 60 and 72 is?
60 = 2^2 x 3 x 5 and 72 = 2^3 x 3^2. The common factors give HCF = 2^2 x 3 = 12.
Simplify 1.1 x 10 + (4.2 – 2) x 3.7?
Brackets first: 4.2 – 2 = 2.2. Then 1.1 x 10 = 11 and 2.2 x 3.7 = 8.14. Total = 19.14.
48km & 600m + 21km & 425m is equal to?
48.600 km + 21.425 km = 70.025 km, that is 70 km and 25 m.
In January morning temperature in Murree was recorded as -3°C and in afternoon it was 11°C. Find the rise in temperature?
The rise from -3 to 11 is 11 – (-3) = 14 degrees.
The cost of 8 math’s books is Rs. 960. Find the cost of 12 math’s books?
8 books cost 960, so one costs 120. Twelve cost 12 x 120 = 1,440.
What is the value of the square root of 16, plus 9?
The square root of 16 is 4, and 4 + 9 = 13. Note this is not the square root of 25.
Two or more fractions with the same denominator are called?
Fractions sharing the same denominator are called like fractions.
Solve this equation 4x + 5 = 17?
4x + 5 = 17 gives 4x = 12, so x = 3.
The perimeter of square whose side is 2.5cm long is?
Perimeter of a square = 4 x side = 4 x 2.5 = 10 cm.
X + 1/X = 2. What is the value of x?
x + 1/x = 2 rearranges to x^2 – 2x + 1 = 0, that is (x-1)^2 = 0, so x = 1.
Sum of Prime Numbers between 60 and 80?
The primes between 60 and 80 are 61, 67, 71, 73 and 79. Their sum is 351.
The outer diameter of metal pipe is 2.84 inch and the inner diameter is 1.94 inches, the thickness of the metal is?
The metal fills the gap on both sides, so thickness = (2.84 – 1.94)/2 = 0.90/2 = 0.45 inch.
Diameter of a circle having radius r is?
The diameter is twice the radius, that is 2r.
15% of what number is 75?
15% of n = 75, so n = 75 / 0.15 = 500.
A cuboid has how many faces?
A cuboid has 6 faces.
If Rs. 782 be divided into three parts proportional to 1/2 : 2/3 : 3/4, then the first part is?
Multiply the ratio 1/2 : 2/3 : 3/4 by 12 to get 6 : 8 : 9, totalling 23 parts. One part = 782/23 = 34, so the first part is 6 x 34 = 204.
The price of a bundle of pens rose from 10 cents to 15 cents. What is the percent increase in price?
The rise is 5 cents on 10, that is 5/10 x 100 = 50%.
Two trains 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?
By 9:00 the first train is 30 km ahead. The second gains 10 km/h, so it catches up in 3 hours. In that time it travels 70 x 3 = 210 km from Rawalpindi.
If part of tank filled in one hour = 1/10, then time required to fill the tank?
If 1/10 of the tank fills in an hour, the whole tank takes 10 hours.
An inlet pipe can fill a tank in 10 hours and an outlet pipe empties the same full tank in 20 hrs. The time required to fill the tank when both pipes are opened?
The inlet adds 1/10 per hour and the outlet removes 1/20, so the net rate is 1/10 – 1/20 = 1/20 per hour, that is 20 hours.
Ali can type at a speed of 25 words per minute. How many words he can type in one hour?
25 words per minute x 60 = 1,500 words per hour.
Pilot School invited same number of boys and girls at its annual party. All came but 15 extra girls showed up. As a result, the ratio of boys to girls is 4:5. How many people did pilot school invite at its party?
If n of each were invited, the girls attending were n + 15. Then n : (n+15) = 4 : 5 gives 5n = 4n + 60, so n = 60. The school invited 60 + 60 = 120 people.
What will be 60% of a number if 80% of it is 320?
80% of the number is 320, so the number is 400. Then 60% of 400 = 240.
If 213×16=3408, then1.6×21.3 is equal to?
1.6 x 21.3 uses the same digits as 16 x 213 = 3,408, with two decimal places, giving 34.08.
If one-third of one-fourth of a number is 15, then three-tenth of that number is?
One third of one quarter is 1/12, so n/12 = 15 and n = 180. Then three tenths of 180 = 54.
45% of 600 is equal to?
45% of 600 = 0.45 x 600 = 270.
What is 1/5% of 6000?
One fifth of one per cent is 0.2% = 0.002. So 0.002 x 6,000 = 12.
A wire of uniform density and composition weighs 16 kg. It is cut into 2 pieces. One is 30 feet and 12 kg. What is the length of the original piece?
The wire has uniform density, so weight is proportional to length. 12 kg corresponds to 30 feet, that is 2.5 feet per kg. The full 16 kg is 16 x 2.5 = 40 feet.
Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are?
Let the total be s. One student scored 0.56s and the other 0.44s, differing by 0.12s = 9, so s = 75. The marks are 42 and 33.
A man bought a flat for Rs. 8,20,000. He borrowed 55% of this money from a bank. How much money did he borrow from the bank?
55% of 820,000 = 0.55 x 820,000 = 451,000.
What is the value of y if 30y = 60?
30y = 60 gives y = 2.
What is the value of x if 2x+9x=11?
2x + 9x = 11x = 11, so x = 1.
If 10 men can construct a building in 40 days, how long will it take 20 men to do this work?
The job is 10 x 40 = 400 man-days, so 20 men take 400/20 = 20 days.
Calculate the following: 313 – 225?
313 – 225 = 88.
Six men working 8 hours a day earn Rs. 720 per week. 8 men working 6 hours a day will earn per week?
Six men at 8 hours give 48 man-hours for 720. Eight men at 6 hours also give 48 man-hours, so the earnings are the same, 720.
What is the value of 10^2?
10^2 = 100.
If 7 – m = 12 – n, then what is m – n?
7 – m = 12 – n rearranges to n – m = 5, so m – n = -5.
4/3 of a number is 22, what is 8/3 of that number?
(4/3)n = 22 gives n = 16.5. Then (8/3) x 16.5 = 44. Note 8/3 is double 4/3, so the answer is simply double 22.
35 kg of Spinach costs Rs. 28. How many kg of spinach can be bought for Rs. 16?
35 kg cost 28 rupees, that is 1.25 kg per rupee. For 16 rupees you get 16 x 1.25 = 20 kg.
If 12 family members spend Rs. 850 in 10 days, then a family of 8 people will spend Rs. 340 in how many days?
12 people over 10 days is 120 person-days for 850, that is 7.083 per person-day. For 8 people spending 340, days = 340 / (8 x 7.083) = 6.
15 cattle can graze a field in 20 days. 20 cattle can graze such field in how many days?
The grazing is 15 x 20 = 300 cattle-days, so 20 cattle take 300/20 = 15 days.
Average of four numbers is 24. What is the sum of the four numbers?
Sum = 24 x 4 = 96.
What percent of 3.5 kg is 70 grams?
3.5 kg = 3,500 g. So 70/3,500 x 100 = 2%.
Square of 32 is?
32 x 32 = 1,024.
24 is split into two parts such that 7 times the first part added to 5 times the second part makes 146. The first part is?
Let the parts be x and 24 – x. Then 7x + 5(24 – x) = 146, so 2x + 120 = 146 and x = 13.
If 4a=8b, what is the ratio of a to b?
4a = 8b gives a = 2b, so a : b = 2 : 1.
A father is twice as old as his son, 20 years ago, the age of the father was 12 times the age of the son. The present age of the father (in years) is?
Let the son be s and father 2s. Twenty years ago, 2s – 20 = 12(s – 20), giving 2s – 20 = 12s – 240. So 10s = 220, s = 22 and the father is 44.
The L.C.M of 2/5, 3/10 and 6/25 is?
For fractions, LCM = LCM of numerators / HCF of denominators = LCM(2,3,6) / HCF(5,10,25) = 6/5.
Find the measure of an angle, if six times its complement is 12° less than twice its supplement?
Let the angle be x. Then 6(90 – x) = 2(180 – x) – 12, so 540 – 6x = 348 – 2x. That gives 4x = 192 and x = 48 degrees.
If h^3=64 then the value of h is?
h^3 = 64 gives h = 4.
If 2x = 32, then x is equal to?
2x = 32 gives x = 16.
3/8 is what part of 1/12?
'What part of' means divide: (3/8) / (1/12) = (3/8) x 12 = 36/8 = 9/2.
The angle between the minute hand and the hour hand of a clock when the time is 4:20 is?
At 4:20 the minute hand is at 120 degrees. The hour hand is at 4 x 30 + 20 x 0.5 = 130 degrees. The angle between them is 10 degrees.
6 Kangaroos eat 6 bags of grass in 6 days. How many Kangaroos will eat 100 bags in 100 days?
6 kangaroos eat 6 bags in 6 days, so one kangaroo eats one bag in 6 days. In 100 days one kangaroo eats 100/6 bags, so to eat 100 bags needs 100 / (100/6) = 6 kangaroos.
In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
Neither red nor green means blue. There are 7 blue out of 8 + 7 + 6 = 21 balls, that is 7/21 = 1/3.
The price of 2.5 dozen eggs is Rs. 75. The price of one egg is?
2.5 dozen = 30 eggs for 75 rupees, so one egg costs 2.5 rupees.
If 16 machines do a piece of work in 4 days, then 8 machines will do the same job in how many days?
The job is 16 x 4 = 64 machine-days, so 8 machines take 64/8 = 8 days.
If the sum of three numbers is 93, then the average of the numbers is?
Average = 93/3 = 31.
The average of the numbers 0.1, 0.21, 0.31, 0.41, 0.51 is?
The sum is 0.1 + 0.21 + 0.31 + 0.41 + 0.51 = 1.54 over 5 values, giving 0.308.
If Rs 1000 is invested at 12% interest and interest is compounded half yearly, what will be the total amount at the end of one year?
Compounded half-yearly means 6% twice: 1,000 x (1.06)^2 = 1,123.60.
Two trades X and Y are paid a total of Rs 550 per week by their employer. If X is paid 120 per cent of the sum paid to Y, how much is Y paid per week?
X = 1.2Y, and X + Y = 550, so 2.2Y = 550 and Y = 250.
The ratio of the number of boys and girls in a college is 7:8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?
Boys 7 become 7 x 1.2 = 8.4 and girls 8 become 8 x 1.1 = 8.8. The new ratio 8.4 : 8.8 = 84 : 88 = 21 : 22.
Rana and Soban work on a job together for four days and complete 60% of it. Rana takes leave then and Soban works for eight more days to complete the job. How long would Rana take to complete the entire job alone?
In 4 days together they finish 60%, so their combined rate is 15% a day. Soban then does the remaining 40% in 8 days, a rate of 5% a day. So Rana does 15 – 5 = 10% a day, taking 10 days alone.
In the sequence 462, 420, 380, X, 306, X stands for?
The differences are -42, -40, -38, -36. So X = 380 – 38 = 342, and 342 – 36 = 306 confirms it.
Ten per cent of twenty plus twenty per cent of ten equals?
10% of 20 = 2 and 20% of 10 = 2, giving 4. Since 2% of 200 = 4, that is the matching expression.
If 70 men can build 4 houses in 12 months, how many men would be required to build 6 houses in 4 months?
One house takes 70 x 12 / 4 = 210 man-months. Six houses need 1,260 man-months, so in 4 months that requires 1,260/4 = 315 men.
If 20 men can do a piece of work in 8 days, how many men will finish it in 10 days?
The job is 20 x 8 = 160 man-days, so in 10 days it needs 160/10 = 16 men.
Pipe “A” can fill a tank in 5 minutes whereas “B” can fill it in 6 minutes. How long would it take both pipes, working together, to fill it?
A fills 1/5 per minute and B 1/6, together 1/5 + 1/6 = 11/30 per minute. The time is 30/11 minutes.
The total of the ages of Amar, Akbar and Anthony is 80 years. What was the total of their ages three years ago?
Each of the three was 3 years younger, so the total was 80 – 9 = 71 years.
A total of 324 coins of 20 paise and 25 paise make a sum of Rs. 71. The number of 25-paise coins is?
Let there be y coins of 25 paise. Then 20(324 – y) + 25y = 7,100, giving 6,480 + 5y = 7,100. So 5y = 620 and y = 124.
If 100 cats kill 100 mice in 100 days, then 4 cats would kill 4 mice in how many days?
100 cats kill 100 mice in 100 days, so one cat kills one mouse in 100 days. Therefore 4 cats kill 4 mice in the same 100 days.
A man completes a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.
Let the journey be d. Then (d/2)/21 + (d/2)/24 = 10, that is d/42 + d/48 = 10. Since 1/42 + 1/48 = 15/336, we get d = 10 x 336/15 = 224 km.
A car travelling with 5/7 of its actual speed covers 42 km in 1 hour 40 min 48 sec. Find the actual speed of the car?
1 hour 40 min 48 sec = 1.68 hours. The reduced speed is 42/1.68 = 25 km/h, which is 5/7 of the actual. So the actual speed = 25 x 7/5 = 35 km/h.
A tailor had a number of shirt pieces to cut from a roll of fabric. He cut each roll of equal length into 10 pieces. He cut at the rate of 45 cuts a minute. How many rolls would be cut in 24 minutes?
Cutting a roll into 10 pieces takes 9 cuts. In 24 minutes he makes 45 x 24 = 1,080 cuts, so 1,080/9 = 120 rolls.
A is 3 years older to B and 3 years younger to C, while B and D are twins. How many years older is C to D?
A = B + 3 and C = A + 3 = B + 6. Since D is B's twin, D = B, so C is 6 years older than D.
4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?
4 weavers make 4 mats in 4 days, so one weaver makes one mat in 4 days. In 8 days each makes 2 mats, so 8 weavers make 16.
In a class, 3/5 of the students are girls and rest are boys. If 2/9 of the girls and 1/4 of the boys are absent, what part of the total number of students is present?
Girls are 3/5 and boys 2/5. Absent girls = (2/9)(3/5) = 2/15, absent boys = (1/4)(2/5) = 1/10. Total absent = 2/15 + 1/10 = 7/30, so present = 23/30.
Two bus tickets from city A to B and three tickets from city A to C cost Rs. 77, but three tickets from city A to B and two tickets from city A to C cost Rs. 73. What are the fares for cities B and C from A?
2b + 3c = 77 and 3b + 2c = 73. Adding gives 5(b+c) = 150, so b + c = 30. Subtracting gives c – b = 4, so c = 17 and b = 13.
A man saves Rs. 500 which is 15% of his annual income. How much does he earn in one year?
500 is 15% of the income, so income = 500 / 0.15 = 3,333.33.
If Rs. 1500 are deducted as income tax at the rate of 10%. What will be the total income?
1,500 is 10% of the income, so income = 1,500 / 0.10 = 15,000.
Daily wages of a worker are increased by 10%. What will be his total daily income if he initially earns Rs. 200?
200 x 1.10 = 220.
What is 3% of 20000?
3% of 20,000 = 0.03 x 20,000 = 600.
If 16 men complete work in 10 days, how many days are required to complete the work by 8 men?
The job is 16 x 10 = 160 man-days, so 8 men take 160/8 = 20 days.
In a school test, if 45% students fail and 550 pass, what is the total number of students?
If 45% fail then 55% pass, and 55% = 550, so the total is 1,000.
If the length of a side of a square is 4cm, calculate its area?
Area of a square = side^2 = 4^2 = 16 square cm.
The length of a rod is 200 cm. Its length increased by 25% due to thermal expansion. The new length will be?
200 x 1.25 = 250 cm.
On selling 17 balls for Rs. 720, there is a loss equal to the cost price of 5 balls. The cost price of one ball is?
Let one ball cost C. Then 17C – 720 = 5C, since the loss equals the cost of 5 balls. So 12C = 720 and C = 60.
A fruit seller had some apples. He sells 40% of the apples and still has 420 apples. How many apples did he originally have?
Selling 40% leaves 60%, which is 420 apples. So the original number = 420 / 0.6 = 700.
Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is?
The numbers are 1.2n and 1.5n, so the ratio is 12 : 15 = 4 : 5.
If 8 men can eat 20 kg of rice in 3 days, how long will 6 men take to eat 40 kg of rice?
8 men eat 20 kg in 3 days, that is 24 man-days for 20 kg, or 0.8333 kg per man-day. For 6 men to eat 40 kg takes 40 / (6 x 0.8333) = 8 days.
A man’s age is three times his son’s. In 15 years, it will be double that of his son’s. How old is the son now?
Let the son be s and the father 3s. In 15 years, 3s + 15 = 2(s + 15), so 3s + 15 = 2s + 30 and s = 15.
About the PPSC Mathematics Past Paper 2018
Every MCQ above is taken from the Punjab Public Service Commission (PPSC) Mathematics papers held in 2018, with the correct answer and a written explanation for each. Past-paper practice is the most dependable way to prepare for PPSC, FPSC, NTS, CSS and PMS, because these papers repeat their themes, and often the questions themselves, from one year to the next.
Questions were checked against reliable sources before publication. Where a circulating source sheet carried a factual or wording error, we corrected it rather than reproducing the mistake. For chapter-wise preparation, work through our Maths MCQs hub, which also lists every other year’s paper. Further reading: Pakistan Movement and the PPSC official website.
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