PPSC Mathematics Past Paper 2022 Solved MCQs with Answers
Solved Mathematics MCQs from the PPSC 2022 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 2022 paper and verified before publication.
According to a time table a coach was due to leave a station at 22.55 and arrive at its destination at 06.05 the next day find the time for the journey?
From 22:55 to midnight is 1 hour 5 minutes, and midnight to 06:05 is 6 hours 5 minutes. Total = 7 hours 10 minutes.
If 94 is subtracted from three times a certain number the result is 36. Find the number?
3n – 94 = 36 gives 3n = 130, so n = 43.33.
A batsman in his 12th innings makes a score of 80 runs and thereby increases his average by 2 runs. Find his average after 12th innings?
Let the average after 12 innings be x. The first 11 averaged x – 2, so 11(x-2) + 80 = 12x. That gives 11x – 22 + 80 = 12x, so x = 58 runs.
Three quantities a, b, c of a:b=1:2, b:c=2:3 then it continues as?
b is 2 in both ratios already, so a : b : c = 1 : 2 : 3 directly.
The area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides?
This is the statement of the theorem of Pythagoras, that the square on the hypotenuse equals the sum of the squares on the other two sides.
If the radius of circle is 1 cm then its area in mm² is?
The radius is 1 cm = 10 mm. Area = pi r^2 = 3.14 x 100 = 314 square mm.
0.75: x =5:8 then the value of x is?
0.75/x = 5/8, so x = 0.75 x 8 / 5 = 1.2.
In a class there are 27 students if there are 7 more girls than boys in the class how many students are girls?
If boys = b then girls = b + 7 and b + (b+7) = 27. So 2b = 20, b = 10 and girls = 17.
The sum of the ages of a father and his son is 100 years now. 5 years ago their ages were in ratio of 2:1. The ratio of the ages of father and son after 10 years will be?
f + s = 100, and five years ago (f-5) = 2(s-5), so f = 2s – 5. Then 3s – 5 = 100, giving s = 35 and f = 65. After 10 years the ages are 75 and 45, that is 5 : 3.
A man annual product sells in 3481600. What is 10% of this amount?
10% of 3,481,600 = 348,160.
A man paid 8500 zakat what will be his total wealth (assuming Zakat is 2.5%)?
Zakat is 2.5% of wealth, so wealth = 8,500 / 0.025 = 340,000.
A tank fills in 0.8 s; in 2 hours how many tanks can be filled?
2 hours = 7,200 seconds. At 0.8 seconds per tank, 7,200 / 0.8 = 9,000 tanks.
If (3a+5b)/(3a-5b)=5, a:b is equal to?
(3a+5b) = 5(3a-5b) gives 3a + 5b = 15a – 25b, so 30b = 12a and a/b = 30/12 = 5/2.
Samar Bought a shirt for Rs.250, sold Rs.295, what is the profit?
Profit = 295 – 250 = 45 rupees.
Reciprocal of sum of reciprocals of 2 & 3?
The reciprocals are 1/2 and 1/3, summing to 5/6. The reciprocal of 5/6 is 6/5.
Ages A:B = 6:5, sum 44; age of B after 8 years?
6k + 5k = 44 gives k = 4, so B is 5 x 4 = 20 now and 20 + 8 = 28 after eight years.
A and B together can complete a piece of work in 15 days and B alone in 20 days, in how many days can A alone complete the work?
A and B do 1/15 per day and B alone does 1/20, so A alone does 1/15 – 1/20 = 1/60, that is 60 days.
When 52416 is divided by 312, the quotient is 168. What will be the quotient when 52.416 is divided by 0.0168?
52.416 / 0.0168 keeps the same digits as 52416 / 16.8. Since 52416 / 312 = 168, we get 52416 / 16.8 = 3,120.
Rs. 1200 is lent out at 5% per annum simple interest for 3 years. Find the amount after 3 years?
SI = 1200 x 5 x 3 / 100 = 180. Amount = 1,200 + 180 = 1,380.
How many times in a day, are the hands of a clock in a straight line but opposite in direction?
The hands point in exactly opposite directions 22 times in 24 hours, that is 11 times in each 12-hour period.
The sum of the squares of two positive integers is 100 and the difference of their squares is 28. The sum of the numbers is?
Adding a^2 + b^2 = 100 and a^2 – b^2 = 28 gives 2a^2 = 128, so a = 8. Then b^2 = 36 and b = 6. Their sum is 14.
A and B can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long would B take alone to do it?
A+B = 1/4, B+C = 1/3, A+C = 1/2. Adding gives 2(A+B+C) = 13/12, so A+B+C = 13/24. Then B = 13/24 – 1/2 = 1/24, that is 24 hours.
A worker is paid Rs. 2130 for 6 days. If his total wage during a month is Rs. 9230, find the number of days he worked in the month.
The daily wage is 2,130 / 6 = 355. Days worked = 9,230 / 355 = 26.
If 3x + 10 = 250, then x = ?
3x + 10 = 250 gives 3x = 240, so x = 80.
There are 56 boys in a class of 140 students. What percent of the students are boys?
56 / 140 x 100 = 40%.
A worker did work for 1 week and 3 days for Rs. 750. In one month (30 days) how much money would he get?
One week and three days is 10 days for 750, so 75 per day. In 30 days he earns 30 x 75 = 2,250.
The original amount 5000 is increased by 6000 in 4 years. How much percent did it increase per year (simple interest)?
The interest earned is 6,000 on 5,000 over 4 years. Rate = 6000 x 100 / (5000 x 4) = 30% per year.
12 water pumps can make a water tank empty in 20 minutes. But 2 pumps are out of order. In how long will the remaining pumps take to make the tank empty?
12 pumps take 20 minutes, so the job is 240 pump-minutes. With 10 working pumps it takes 240/10 = 24 minutes.
Ali earns Rs 7500 in 2 weeks. What will he earn in 2 days if he works 6 days a week?
Two weeks is 12 working days at 6 days a week, so the daily wage is 7,500/12 = 625. Two days give 1,250.
A is 4 times as fast as B and therefore is able to finish the work in 45 days less than B. A and B, can complete the work in how many days?
If B takes t days then A takes t/4, and t – t/4 = 45 gives 3t/4 = 45, so t = 60 and A takes 15. Together they do 1/60 + 1/15 = 1/12 per day, that is 12 days.
Two trains are running in opposite directions with speeds of 62 km/h and 40 km/h respectively. If the length of one train is 260 m, and they cross each other in 18 seconds, then what is the length of the other train?
Relative speed = 62 + 40 = 102 km/h = 28.33 m/s. In 18 seconds they cover 510 m, which is the sum of both lengths. So the other train is 510 – 260 = 250 m.
The price of 357 mangoes is Rs.1517.25. What will be the approximate price of 49 dozen of such mangoes?
Price per mango = 1517.25 / 357 = 4.25. 49 dozen = 588 mangoes, costing 588 x 4.25 = 2,499.
A rectangular lawn 80 meters by 60 meters has two roads each 10 m wide running in the middle of it, one parallel to the length and the other parallel to the breadth. Find the cost of gravelling at the Rate of Rs. 30 per square meter?
The two roads cover 80 x 10 + 60 x 10 minus the 10 x 10 overlap counted twice, that is 800 + 600 – 100 = 1,300 sq m. Cost = 1,300 x 30 = 39,000.
The average run of a cricket player in 10 innings was 33. How many runs must he make in his next innings so as to increase his average by 3?
Ten innings at 33 give 330 runs. To average 36 over 11 innings he needs 396, so the next innings must be 66.
The average income of A and B is 50000 and average income of B and C is 60000 and Average income of A and C is 55000. What is the income of B?
A+B = 100,000, B+C = 120,000, A+C = 110,000. Adding gives 2(A+B+C) = 330,000, so the total is 165,000. Then B = 165,000 – 110,000 = 55,000.
Prize money Rs. 60,000 will be distributed among eight teams such that the prize money forms an arithmetic progression. If the last place team is given Rs 4,000, how much is awarded to the first place team?
For an A.P. the sum = n/2 (first + last), so 60,000 = 8/2 x (a + 4,000) = 4(a + 4,000). Then a + 4,000 = 15,000 and a = 11,000.
A carpenter lays x bricks per hour for y hours and then lays x/2 bricks per hour for 2y more hours. How many bricks total?
First stage: x bricks per hour for y hours = xy. Second stage: x/2 per hour for 2y hours = xy. Total = 2xy.
The place value of 9 in 0.06945 is?
In 0.06945 the digits after the point are 0 tenths, 6 hundredths, 9 thousandths. So the place value of 9 is 0.009.
The average age of 20 students is 12 years. If the teacher is included, the average increases by one. The age of the teacher is?
20 students at 12 years total 240. With the teacher there are 21 people averaging 13, a total of 273. The teacher is 273 – 240 = 33.
7.5 million in numbers is written as?
7.5 million = 7.5 x 1,000,000 = 7,500,000.
The expression (a+b)(a² – ab + b²) is equal to:
This is the standard identity (a+b)(a^2 – ab + b^2) = a^3 + b^3.
For x: y = 3:4, then (7x+3y):(7x-3y) is equal to?
Let x = 3k and y = 4k. Then (21k + 12k) : (21k – 12k) = 33k : 9k = 11 : 3.
What will be the compound interest on a sum of Rs. 1875 after 2 years if the rate of interest for the first year is 4% and that for the second year is 8%?
After year one: 1875 x 1.04 = 1,950. After year two: 1,950 x 1.08 = 2,106. Compound interest = 2,106 – 1,875 = 231.
The mean weight of 100 students in a class is 46 kg. The mean weight of boys is 50 kg and that of girls is 40 kg. Therefore, the number of boys is?
If b boys and (100-b) girls, then 50b + 40(100-b) = 46 x 100 = 4,600. So 10b = 600 and b = 60.
A and B together can complete a work in 3 days. They start together but, after 2 days, B left the work. If the work is completed after 2 more days, B alone could do the work in?
A and B do 1/3 per day, so in 2 days they finish 2/3. A alone completes the remaining 1/3 in 2 days, so A does 1/6 per day. Then B = 1/3 – 1/6 = 1/6, that is 6 days.
The average of the first five multiples of 9 is?
The first five multiples of 9 are 9, 18, 27, 36, 45. Their average is the middle value, 27.
A man takes 6 hours 15 minutes in walking a distance and riding back; both-way walk is 7 hours 45 minutes. Time to ride both ways is?
Walking one way plus riding one way takes 6h15m. Walking both ways takes 7h45m, so one walk is 3h52.5m. One ride = 6h15m – 3h52.5m = 2h22.5m, so riding both ways takes 4h45m.
If the price of a commodity is increased by 50%, by what fraction must consumption be reduced to keep expenditure same?
After a 50% rise the price is 1.5 times, so consumption must fall to 1/1.5 = 2/3, a reduction of 1/3.
The price of a bicycle is rupees 6480 inclusive 8% GST what is the original price of the bicycle?
The price includes 8% GST, so original = 6,480 / 1.08 = 6,000.
From 2008 to 2009, the sales of a book decreased by 80%. If the sale in 2010 was same as in 2008, by what per cent did it increase from 2009 to 2010?
An 80% fall takes 100 down to 20. Returning to 100 is an increase of 80 on a base of 20, that is 400%.
The price of an article is cut by 20%. In order to restore the reduced price to the original value, by how much must the reduced price be increased?
A 20% cut takes 100 to 80. Restoring to 100 needs an increase of 20 on 80, that is 25%.
If a heart beats 72 times in one minute, then how many seconds it beats 210 times?
72 beats take 60 seconds, so 210 beats take 210 x 60 / 72 = 175 seconds.
A person bought a camera for Rs 1800 and sold it for 10% loss. How much price did he finally get?
A 10% loss leaves 90% of cost: 1,800 x 0.9 = 1,620.
A project of construction of a building can be completed by 150 workers in 40 days. But project manager brought 30 more workers after 16 days. In how many days will the remaining work be finished?
The project is 150 x 40 = 6,000 worker-days. In 16 days, 150 x 16 = 2,400 are done, leaving 3,600. With 180 workers this takes 3,600/180 = 20 days.
30% of a number when subtracted from 91, gives the number itself. Find the number?
91 – 0.30n = n gives 91 = 1.30n, so n = 70.
The average of 6 numbers is 30. If the average of the first four is 25 and that of the last three is 35, the fourth number is?
Six numbers average 30, a total of 180. The first four total 100 and the last three total 105. Adding those counts the fourth number twice, so it equals 100 + 105 – 180 = 25.
A and B have the same amount of money at first. After A gave B $50, B had 5 times as much money as A had left. How much do A and B have at first?
Let each start with x. After A gives 50, A has x-50 and B has x+50. Then x + 50 = 5(x – 50), so 4x = 300 and x = 75.
Three-fifth of students speak Spanish and one-fourth speaks Italian. What percentage speaks French? (Assume only these three languages are spoken)
Spanish and Italian together are 3/5 + 1/4 = 17/20. French takes the remaining 3/20 = 15%.
Each day, Robert eats 40% of the pistachios left in his jar at that time. At the end of the second day 27 pistachios remain. How many pistachios were in the jar at the start of the first day?
Eating 40% leaves 60% each day, so after two days 0.6 x 0.6 = 0.36 of the original remains. Then 0.36n = 27 gives n = 75.
Salman bought a TV for Rs. 8,800 including GST at 10%. What is the original cost of the TV?
Including 10% GST the price is 1.1 times the original, so original = 8,800 / 1.1 = 8,000.
Aaron has 3 times as much money as Josh. If Aaron gives Josh $50, Josh will then have as much money as Aaron. How much money do two of them have together?
Let Josh have j, so Aaron has 3j. After the gift, 3j – 50 = j + 50, giving 2j = 100 and j = 50. Aaron has 150, so together they have 200.
The cost of 5kg tomatoes is Rs. 80. What will be the cost of 8kg?
5 kg costs 80, so 1 kg costs 16 and 8 kg costs 128.
If Rs. 4 becomes Rs. 10 in 50 years at simple interest then the rate of interest is?
Interest = 10 – 4 = 6 on a principal of 4 over 50 years. Rate = 6 x 100 / (4 x 50) = 3%.
On a certain item the price is decreased to 0.42 from 0.62. What is the actual percentage of discount?
The fall is 0.62 – 0.42 = 0.20. As a percentage of the original, 0.20/0.62 x 100 = 32%.
The price of an article is Rs. 945 with 5% GST. The original price of the article is?
The price includes 5% GST, so original = 945 / 1.05 = 900.
Given the function f(x) = -3x² – 2x + 1, find f(1).
f(1) = -3(1)^2 – 2(1) + 1 = -3 – 2 + 1 = -4.
A garrison has provision for 30 days for a certain number of men. If 2/3 of them do not attend the mess, then the food will last for?
If only one third eat, the food lasts three times as long: 3 x 30 = 90 days.
What is meant by a linear equation?
A linear equation is an equation of degree one, in which the highest power of the variable is 1.
If 1/2 inch is equal to 12 kilometers. The distance between two points is 5-2/3 inches. What is the distance in kilometers?
If half an inch is 12 km then one inch is 24 km. The distance 5 and 2/3 inches = 17/3 x 24 = 136 km.
Four people live in a house. There are 22 houses in one street. How many people live in the street?
4 people per house x 22 houses = 88 people.
About the PPSC Mathematics Past Paper 2022
Every MCQ above is taken from the Punjab Public Service Commission (PPSC) Mathematics papers held in 2022, 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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