PPSC Mathematics Past Paper 2021 Solved MCQs with Answers
Solved Mathematics MCQs from the PPSC 2021 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 2021 paper and verified before publication.
A train left a station at 8.35 a.m. and arrived at destination at 3.12 p.m. How long did the journey take?
From 8:35 a.m. to 3:12 p.m. is 6 hours to 2:35 p.m. plus 37 minutes, that is 6 hours 37 minutes.
The value of an article is 12000. Each year it depreciates by 5%. What will be the value of the article after 4 years?
Depreciating 5% a year leaves 95% each year: 12,000 x (0.95)^4 = 12,000 x 0.8145 = 9,774.
The strength of a class is 6000 in 1994. What was the enrollment in 1970 if enrollment doubled every 8 years?
From 1970 to 1994 is 24 years, that is three doublings. So the 1970 figure = 6,000 / 2^3 = 6,000/8 = 750.
The sum of five consecutive even numbers of set X is 440. Find the sum of a different set of five consecutive integers whose second least number is 121 less than double the least number of set X?
Five consecutive even numbers summing to 440 have middle 88, so they are 84 to 92 and the least is 84. Double that is 168, and 121 less is 47. So the new set has second least 47, meaning it starts at 46: 46+47+48+49+50 = 240.
A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8 g/cm³, then the weight of iron is?
External radius 4 cm, internal radius 3 cm. Volume = pi(16-9) x 21 = (22/7) x 7 x 21 = 462 cubic cm. Weight = 462 x 8 = 3,696 g = 3.696 kg.
The value of (3.5 x 1.4) + 0.7 is?
3.5 x 1.4 = 4.9, and 4.9 + 0.7 = 5.6.
15 men were hired to plough a piece of land in 10 days. How many more men will be required to do the same job in 3 days?
The job is 15 x 10 = 150 man-days. To finish in 3 days needs 150/3 = 50 men, that is 35 more than the 15 already hired.
The sum of two numbers is 40 and their difference is 4. The ratio of the numbers is?
The numbers are (40+4)/2 = 22 and (40-4)/2 = 18. The ratio 22 : 18 simplifies to 11 : 9.
The product of two numbers is 72. Find the other number when one number is 9?
72 / 9 = 8.
If x² – y² = 28 and x – y = 8, then the average of x and y is?
x^2 – y^2 = (x+y)(x-y) = 28. Since x – y = 8, x + y = 3.5. The average is 3.5/2 = 1.75.
If x – 4 = 11, then the value of x – 8 is?
x – 4 = 11 gives x = 15, so x – 8 = 7.
Saeed receives a commission of Rs. 25 for every Rs. 250 worth of merchandise he sells. What is the percentage(%) of his commission?
25 / 250 x 100 = 10%.
At 3:00 AM the temperature was 13°C below zero and by noon it was 32°C; the average hourly increase was?
The temperature rises from -13 to 32, a change of 45 degrees, over the 9 hours from 3 a.m. to noon. So the hourly rise is 45/9 = 5 degrees.
If 4 out of 25 candidates failed a driving test, the percentage of pass candidates is?
If 4 of 25 failed, 21 passed. 21/25 x 100 = 84%.
The average of 50 numbers is 30. If 35 and 25 are removed, what is the new average?
The 50 numbers total 50 x 30 = 1,500. Removing 35 and 25 takes away 60, leaving 1,440 over 48 numbers, that is 30 again.
A sum of money doubles in 3 years at compound interest compound annually. In how many years will it become four times of itself at the same rate?
Doubling takes 3 years, and four times is two doublings, so it takes 2 x 3 = 6 years.
If 60 women spin 48 kg in 8 hours, how much will 30 women spin in 12 hours?
Rate = 48 / (60 x 8) = 0.1 kg per woman-hour. Then 30 women for 12 hours spin 30 x 12 x 0.1 = 36 kg.
The average of 10 innings is 32. How many runs must a player score in the next innings to raise the average by 4?
Ten innings at 32 give 320 runs. To average 36 over 11 innings needs 396, so the next innings must be 76.
If 500 kg of meat feeds 20 lions for a week, for how many days will 200 kg feed 14 lions?
500 kg feeds 20 lions for 7 days, that is 140 lion-days, so 3.571 kg per lion-day. Then 200 kg feeds 14 lions for 200 / (14 x 3.571) = 4 days.
If the original price of an item is Rs. 75, what is the price after a 15% discount?
A 15% discount leaves 85%: 75 x 0.85 = 63.75.
If x = 3 + √8, what is the value of x² + 1/x²?
If x = 3 + sqrt8 = 3 + 2sqrt2, then 1/x = 3 – 2sqrt2, so x + 1/x = 6. Then x^2 + 1/x^2 = (x + 1/x)^2 – 2 = 36 – 2 = 34.
A 162 Km long road can be constructed in 9 months. How many months are required to construct a 306 Km long road?
The work scales with length: 306/162 x 9 = 17 months.
A person bought an item for Rs.2500 and sold it at a 15% discount on the cost price. What was the selling price?
A 15% reduction on 2,500 leaves 2,500 x 0.85 = 2,125.
If 10 persons can do a work in 20 days, then 20 persons with twice the efficiency can do the same work in?
The job is 10 x 20 = 200 person-days. Twenty people at twice the efficiency count as 40, so 200/40 = 5 days.
Hassan borrowed 5000 with simple interest for five years. He paid an extra 500. What percent per annum did he pay?
SI = 500 on a principal of 5,000 over 5 years. Rate = 500 x 100 / (5000 x 5) = 2%.
A and B can do a piece of work in 12 days, B and C in 15 days, A and C in 20 days. How many days will A, B and C together take to finish the work?
A+B = 1/12, B+C = 1/15, A+C = 1/20. Adding gives 2(A+B+C) = 1/5, so A+B+C = 1/10, that is 10 days.
Working 5 hours a day, A can complete a work in 8 days. Working 6 hours a day, B can complete the same work in 10 days. Working 8 hours a day, in how many days can they jointly complete the work?
A needs 5 x 8 = 40 hours and B needs 6 x 10 = 60 hours. Together they do 1/40 + 1/60 = 1/24 per hour. At 8 hours a day that is 1/3 per day, so 3 days.
Simplify: 1/log_3(60) + 1/log_4(60) + 1/log_5(60)
Using the change of base rule, 1/log_a(60) = log_60(a). So the sum is log_60(3) + log_60(4) + log_60(5) = log_60(60) = 1.
Two high tides and two low tides of nearly equal level each lunar day is called?
A tidal pattern with two nearly equal high tides and two low tides each lunar day is called a semidiurnal tide.
The average age of 3 friends is 23. Even if the age of a 4th friend is added, the average remains 23. What is the age of the 4th friend?
Since the average stays at 23 when a fourth person is added, that person must be exactly the average, 23 years.
A man walked for 1/3 hour and then got an automobile ride for 1/2 hour. What part of the total time consumed did he ride on the automobile?
Total time = 1/3 + 1/2 = 5/6 hour. The ride is (1/2)/(5/6) = 3/5 of the total.
A person sold a pen at Rs 900 with a 25% loss. What was the original price?
A 25% loss means the sale price is 75% of cost, so cost = 900 / 0.75 = 1,200.
Rs.1200 was lent at 5% p.a. simple interest for 3 years. What is the total amount after 3 years?
SI = 1200 x 5 x 3 / 100 = 180, so the amount is 1,200 + 180 = 1,380.
Aslam bought a cycle for Rs 750 and sold it for Rs 675. Find the loss percentage?
Loss = 750 – 675 = 75. Percentage = 75/750 x 100 = 10%.
The mean proportional between 2 and 8 is?
The mean proportional between a and b is sqrt(ab) = sqrt(16) = 4.
If A:B = 3:4 and B:C = 12:13, then A:C is?
A : B = 3 : 4 = 9 : 12, and B : C = 12 : 13. With B common at 12, A : C = 9 : 13.
Sum of two numbers is 37; difference of their squares is 185. Difference of numbers?
The difference of squares factorises: (a+b)(a-b) = 185. Since a + b = 37, a – b = 185/37 = 5.
Avg age of A-E is 40; avg of A&B is 35; avg of C&D is 42. Age of E?
Five people average 40, a total of 200. A+B = 70 and C+D = 84, so E = 200 – 70 – 84 = 46.
A 36” strip shrinks to 33” after washing. If it were 48”, after washing it remains?
The strip shrinks in the ratio 33/36 = 11/12. So 48 inches becomes 48 x 11/12 = 44 inches.
What is the ratio in Rs 2.80 and 40 paisa?
Rs 2.80 is 280 paisa. The ratio 280 : 40 simplifies to 7 : 1.
The salaries of A, B and C are in the ratio 1:3: 4. If the salaries are increased by 5%, 10% and 15% respectively, then the increased salaries will be in the ratio?
Salaries 1 : 3 : 4 become 1.05 : 3.30 : 4.60 after the rises. Multiplying by 20 gives 21 : 66 : 92.
The average of five numbers is 27. If one number is excluded, the average becomes 25. The excluded number is?
Five numbers average 27, a total of 135. Four numbers averaging 25 total 100, so the excluded number is 35.
There are two sections A and B of a class, consisting of 36 and 44 students respectively. If the average weight of section A is 40kg and that of section B is 35kg, find the average weight of the whole class?
Total weight = 36 x 40 + 44 x 35 = 1,440 + 1,540 = 2,980 kg over 80 students, giving 37.25 kg.
Three-fourth of a number is 60 more than its one-third. The number is?
(3/4)n = (1/3)n + 60. Since 3/4 – 1/3 = 5/12, we get (5/12)n = 60 and n = 144.
4.036 divide by 0.04?
4.036 / 0.04 = 403.6 / 4 = 100.9.
The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is?
The foot is the adjacent side, so cos(60) = 4.6 / L. Since cos(60) = 0.5, L = 4.6 / 0.5 = 9.2 m.
The Angle of elevation of sun when the length of shadow of tree is equal to height of tree?
When the shadow equals the height, tan(angle) = height/shadow = 1, so the angle is 45 degrees.
If 3x + 7 = 250, then what is x?
3x + 7 = 250 gives 3x = 243, so x = 81.
If x : y = 5 : 2, then (8x + 9y) : (8x + 2y) is equal to?
Let x = 5k and y = 2k. Then (40k + 18k) : (40k + 4k) = 58k : 44k = 29 : 22.
If a number is multiplied by two-third of itself and equals 864, the number is?
n x (2/3)n = 864 gives (2/3)n^2 = 864, so n^2 = 1,296 and n = 36.
In How many ways a President, Vice President and a water boy can be selected from a group of ten people?
The three posts are distinct, so order matters and this is a permutation: 10P3 ways.
A student obtains 75%, 80% and 85% in three subjects. When a fourth subject is added, the average cannot be less than what?
The three marks total 240. In the worst case the fourth subject scores 0, giving an average of 240/4 = 60%. So the average cannot fall below 60%.
A sum of Rs. 12,500 amounts to Rs. 15,500 in 2 years (simple interest). Rate of interest?
SI = 15,500 – 12,500 = 3,000. Rate = 3,000 x 100 / (12,500 x 2) = 12%.
If x% of 225 is 150 then x?
x% of 225 = 150 gives x = 150 x 100 / 225 = 66.67%.
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?
Let the numbers be 3k and 5k. Then (3k-9)/(5k-9) = 12/23, giving 69k – 207 = 60k – 108, so 9k = 99 and k = 11. The smaller number is 3 x 11 = 33.
Two numbers are, respectively, 60 percent and 20 percent more than a third number. What percent is the second of the first?
Take the third number as 100. The first is 160 and the second is 120. So the second as a percentage of the first is 120/160 x 100 = 75%.
What is the average of the numbers: 0, 0, 4, 10,5, and 5?
The sum is 0 + 0 + 4 + 10 + 5 + 5 = 24 over 6 values, giving an average of 4.
0.0009 +x = 0.01. Find the value of x?
x = 0.01 – 0.0009 = 0.0091.
The area of a circle is 98.56 cm². Find its circumference?
Area = pi r^2 = 98.56, so r^2 = 98.56 x 7/22 = 31.36 and r = 5.6 cm. Circumference = 2 x (22/7) x 5.6 = 35.2 cm, given as 35.17.
A class had 14 boys with an average height of 5.3 feet. A new boy joined the class. Now the average of 15 boys in the class was 5.25 feet. Find the height of the new boy?
14 boys total 14 x 5.3 = 74.2 feet. Fifteen boys at 5.25 total 78.75, so the new boy is 78.75 – 74.2 = 4.55 feet.
A car consumes 20 liters of petrol to drive 240 kilometers. How many liters of petrol will be required for a trip of 600 kilometers?
The car uses 20 litres per 240 km. For 600 km it needs 600 x 20 / 240 = 50 litres.
An alarm beeps 16 times per minute, how much time will it take to beep 88 times?
At 16 beeps per minute, 88 beeps take 88/16 = 5.5 minutes, that is 5 minutes 30 seconds.
The average (arithmetic mean) of 5, 10, 15 and x is 20. What is the value of x?
(5 + 10 + 15 + x)/4 = 20 gives 30 + x = 80, so x = 50.
Simplify: 0.8-0.3+0.5?
0.8 – 0.3 + 0.5 = 1.0.
What percent of 40 is 15?
15/40 x 100 = 37.5%.
A ran around a 1/4 kilometer track 17 times. How many kilometers did he ran?
17 laps of a quarter kilometre = 17 x 0.25 = 4.25 km.
2:x=x:50 what one number can replace x?
2 : x = x : 50 means x^2 = 100, so x = 10.
Express 1/2 as a percentage.
1/2 = 0.5 = 50%.
Divide 5/14 with 7/10?
Dividing by a fraction means multiplying by its reciprocal: (5/14) x (10/7) = 50/98 = 25/49.
The square root of 729 is?
27 x 27 = 729, so the square root of 729 is 27.
If 15 men can manufacture 27 baskets in an hour then how many baskets will 45 men make in 40 minutes?
15 men make 27 baskets an hour, that is 1.8 per man-hour. 45 men for 40 minutes give 45 x (2/3) = 30 man-hours, producing 30 x 1.8 = 54 baskets.
If q=56 and r=37, then what is (q²-r²)/(q-r)?
(q^2 – r^2)/(q – r) = (q+r)(q-r)/(q-r) = q + r = 56 + 37 = 93.
Simplify: 13.05 x 4.5 + 0.5?
13.05 x 4.5 = 58.725, and adding 0.5 gives 59.225.
If 3/17 of a number is 51, what is 2/17 of that number?
If 3/17 of n is 51 then n = 51 x 17/3 = 289. Then 2/17 of 289 = 34.
If 25% proposals are rejected for a project, what is the ratio of the number of proposals accepted to number of proposals rejected?
If 25% are rejected then 75% are accepted, so accepted : rejected = 75 : 25 = 3 : 1.
If 50 masons can build a wall in 12 days, how many days will 25 masons take to build the same?
The job is 50 x 12 = 600 mason-days, so 25 masons need 600/25 = 24 days.
A concrete required 15 bags of cement and 18 bags of sand. If only 10 bags of cement are used, how much sand is required to make the concrete?
Cement and sand are in the ratio 15 : 18. With 10 bags of cement the sand needed = 10 x 18/15 = 12 bags.
The total population of a city is 6500. The number of males and females increases by 5% and 10% respectively and consequently the population becomes 7000. Find the number of males in the city?
Let males be m. Then 1.05m + 1.10(6500 – m) = 7,000, giving 7,150 – 0.05m = 7,000. So 0.05m = 150 and m = 3,000.
If 25% of a is 50% of b, then b is what percent of a?
0.25a = 0.5b gives b = 0.5a, so b is 50% of a.
If the rate of tax on salary is 15%, then what is the monthly salary of a person who pays Rs. 4500 per month as tax?
Tax is 15% of salary, so salary = 4,500 / 0.15 = 30,000.
Price of a commodity is increased from Rs. 40 to Rs. 50 in a local market. What percentage was this increase?
The rise is 50 – 40 = 10 on a base of 40, that is 10/40 x 100 = 25%.
The mean of 5 observations is 60, the mean of 10 observations is 30 and mean of 15 observations is 20. The mean of all 30 observations is?
The totals are 5 x 60 = 300, 10 x 30 = 300 and 15 x 20 = 300, summing to 900 over 30 observations. The mean is 900/30 = 30.
The sum of all even numbers up to 100 is?
The even numbers 2 to 100 form 50 terms averaging 51, so the sum is 50 x 51 = 2,550.
Amna has twice as much money as Maryam. Maryam has 50% more money than Sara. If the average money with them is 110, then Amna has?
Let Sara have S. Then Maryam has 1.5S and Amna has 3S. The average is (3S + 1.5S + S)/3 = 5.5S/3 = 110, so S = 60 and Amna has 180.
About the PPSC Mathematics Past Paper 2021
Every MCQ above is taken from the Punjab Public Service Commission (PPSC) Mathematics papers held in 2021, 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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