PPSC Mathematics Past Paper 2020 Solved MCQs with Answers
Solved Mathematics MCQs from the PPSC 2020 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 2020 paper and verified before publication.
Average age of A and B is 30 years, that of B and C is 32 years and the average age of C and A is 34 years. The age of C is?
A+B = 60, B+C = 64 and C+A = 68. Adding gives 2(A+B+C) = 192, so the total is 96. Then C = 96 – 60 = 36 years.
In an examination, 1100 boys and 900 girls appeared, 50% of the boys and 40% of the girls passed. The fail percentage is?
Passes = 50% of 1,100 + 40% of 900 = 550 + 360 = 910 out of 2,000. So failures = 1,090/2,000 = 54.5%.
The square of standard deviation is called?
The square of the standard deviation is called the variance.
60 men can do a work in 40 days. How long will it take 40 men to complete the same work?
The work is 60 x 40 = 2,400 man-days, so 40 men need 2,400/40 = 60 days.
What is the value of x in 3x -15-6= 0?
3x – 15 – 6 = 0 gives 3x = 21, so x = 7.
If Rs. 1000 is divided amongst Rabail and Amna in the proportion of 2:3 respectively, how much will Rabail receive?
In the ratio 2 : 3 the parts total 5, so Rabail gets 2/5 x 1,000 = 400.
A Mason fixed black tiles of square shape around a square room. There are 21 tiles on each side of the room. How many tiles did he need altogether?
Tiles run round the border only. With 21 on each side, the total is 4 x 21 – 4 = 80, subtracting the four corners counted twice.
A rectangle has a length of 10cm and a perimeter of 30cm. Find the width of the rectangle?
Perimeter = 2(l + w), so 30 = 2(10 + w). Then 10 + w = 15 and w = 5 cm.
A car is moving with the speed of 120 km/h. How much distance does the car cover in 4 hours and 30 minutes?
4 hours 30 minutes is 4.5 hours, so distance = 120 x 4.5 = 540 km.
If books bought at prices ranging from Rs. 150 to Rs. 300 are sold at prices ranging from Rs. 250 to Rs. 350, what is the greatest possible profit that might be made in selling 15 books?
The greatest profit per book is the highest selling price minus the lowest cost: 350 – 150 = 200. For 15 books that is 3,000.
The cost of paint is Rs. 36.50 per kg. If one kg of paint covers 16 square feet, how much will it cost to paint outside of a cube having each side of 8 feet?
A cube of side 8 has surface area 6 x 64 = 384 sq ft. At 16 sq ft per kg that needs 24 kg, costing 24 x 36.50 = 876.
Divide 350 into two parts in the way that one exceeds the other by 4?
If the parts differ by 4, the larger is (350+4)/2 = 177 and the smaller is 173.
The circumference of a circle whose diameter is 7 inches is approximately?
Circumference = pi x diameter = (22/7) x 7 = 22 inches.
If one of the angles of a triangle is 90 degrees what would be the sum of the other two angles?
The angles of a triangle sum to 180. With one angle 90, the other two sum to 90 degrees.
If the amount of 15 percent of sales tax paid on an article comes to Rs. 1500, what is the actual price of the article?
15% of the price is 1,500, so the price = 1,500 / 0.15 = 10,000.
Find the marked price of a uniform shirt if it is sold for Rs. 1311 after a discount of 5%?
After a 5% discount the price is 95% of the marked price, so marked price = 1,311 / 0.95 = 1,380.
If Amir is in the North of Bilal and Saad is in the West of Bilal. In which direction is Amir with respect to Saad?
Amir is north of Bilal and Saad is west of Bilal, so from Saad's position Amir lies to the north and east, that is north-east.
The mean proportional of 4 and 16 is?
The mean proportional between 4 and 16 is sqrt(4 x 16) = sqrt(64) = 8.
The total distance from school to house is 39 km. Abid covered a distance of 13 km. What percentage of the whole distance has he covered?
13 / 39 x 100 = 33.33%.
A cyclist covers a distance of 750 meters in 2 minutes and 30 seconds. What is his speed in km/hr?
2 minutes 30 seconds = 150 seconds. Speed = 750/150 = 5 m/s = 5 x 3.6 = 18 km/h.
Six tenths is the same as?
Six tenths = 6/10 = 0.6.
When a student weighing 45 kgs left a class, the average weight of the remaining 59 students increased by 200g. What is the average weight of the remaining 59 students?
Let the new average be x, so the original 60 averaged x – 0.2. Then 60(x – 0.2) – 45 = 59x, giving 60x – 12 – 45 = 59x, so x = 57 kg.
Solve: 100 ÷ 50 × 2?
Working left to right: 100 divided by 50 = 2, then 2 x 2 = 4.
If a man's salary is increased by 1/5 and his current pay is 60000. What will be his new salary?
An increase of 1/5 makes the salary 6/5 of the original: 60,000 x 1.2 = 72,000.
Solve: 1/10 × 3/5 × 6/5?
(1/10) x (3/5) x (6/5) = 18/250 = 9/125.
If 1 inch = 60 units, then 2.5 inches is equal to?
2.5 x 60 = 150 units.
294 is multiplied by which positive integer to give a complete square?
294 = 2 x 3 x 7^2. To make a perfect square the factors 2 and 3 must be paired, so multiply by 6.
A chemical solution has 8% acid. If the acid content is 15 ml, the total volume of the solution is?
8% of the volume is 15 ml, so the total = 15 / 0.08 = 187.5 ml.
42 women can do a piece of work in 18 days. How many women would be required to do the same piece of work in 21 days?
The work is 42 x 18 = 756 woman-days. In 21 days that needs 756/21 = 36 women.
Multiply: 9.5 × 6?
9.5 x 6 = 57.
A farmer bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?
Buying 6 for a rupee means the cost is 1/6 each. For a 20% gain the selling price must be 1.2/6 = 0.2 each, so he sells 1/0.2 = 5 for a rupee.
A shopkeeper raises the price of a cycle by 5 percent above the market price and charges 12 percent sales tax on the market price. As a result, a customer has to pay Rs. 4680 for the cycle. What is the market price of the cycle?
The customer pays the market price plus 5% plus 12% tax on the market price, that is 1.17m = 4,680. So m = 4,000.
The cash difference between the selling prices of an article at a profit of 4% and 6% is Rs 3. The ratio of the two selling prices is?
The selling prices are 1.04C and 1.06C, differing by 0.02C = 3, so C = 150. The ratio is 1.04 : 1.06 = 52 : 53.
To fill a tank 25 buckets of water are required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present capacity?
Reducing the bucket to 2/5 of its size means more buckets are needed: 25 / (2/5) = 25 x 5/2 = 62.5.
If the average of five numbers is 6.92, then the sum of numbers is?
Sum = average x count = 6.92 x 5 = 34.6.
The sum of ages of 5 children born at intervals of 3 years each is 50 years. What is the age of the youngest child?
The ages are a, a+3, a+6, a+9, a+12, totalling 5a + 30 = 50. So a = 4 years.
A hockey team won 6 games and lost 8. What is the ratio of wins to the total number of games?
Total games = 6 + 8 = 14. Wins to total = 6 : 14 = 3 : 7.
The 4% of a number is 120, the number is?
4% of n = 120, so n = 120 / 0.04 = 3,000.
A is the father of B but B is not A’s son. What is the relationship of B to A?
A is the father of B, but B is not a son, so B must be a daughter.
If the sum of two numbers is 30 and their difference is 8, what is their product?
The numbers are (30+8)/2 = 19 and (30-8)/2 = 11. Their product is 209.
Think of a number, divide it by 4 and add 9 to it. If the result is 15, what is the number?
n/4 + 9 = 15 gives n/4 = 6, so n = 24.
Which one of the following is a positive square root of 2209?
47 x 47 = 2,209, so the positive square root is 47.
Complete the series: 1, 3, 7, 15, 31, 63, __?
Each term is one less than a power of 2: 2^1-1, 2^2-1, 2^3-1 and so on. The next is 2^7 – 1 = 127. Equivalently, double and add one.
2^5 means?
2^5 means 2 multiplied by itself five times: 2 x 2 x 2 x 2 x 2 = 32.
LCM stands for?
LCM stands for Least Common Multiple.
If Ali get 25% profit by selling an article in 250 rupees what is the original price of the article?
A 25% profit means the selling price is 1.25 times cost, so cost = 250 / 1.25 = 200.
Ahmed got 25 rupees profit on every article of Rs 250 then how much percentage of profit he got?
25 profit on a cost of 250 is 25/250 x 100 = 10%.
Akram sold a plot at Rs 60,000 and the cost of the plot is Rs 57,000 then the profit he earns is?
Profit = 60,000 – 57,000 = 3,000.
If A’s income is 40% less than B’s income, then how much percent is B’s income more than A’s income?
If B earns 100 then A earns 60. B exceeds A by 40 out of 60, that is 40/60 x 100 = 66.67%.
A train is 130 m long it travels at a speed of 45 km/hr. It crosses a bridge in 30 seconds. The Length of Bridge is?
45 km/h = 12.5 m/s. In 30 seconds the train covers 375 m, which is the train plus the bridge. So the bridge is 375 – 130 = 245 m.
If the interest rate of Rs 800 be more than the interest on Rs 400 by Rs 40 in 2 years then the rate of interest per annum is?
The interest difference comes from the extra 400 of principal over 2 years: 400 x r x 2 / 100 = 40, so 8r = 40 and r = 5%.
21 Binders can bind 1400 Books in 15 days. How many Binders will be required to bound 800 books in 20 days?
Rate = 1,400 / (21 x 15) = 4.44 books per binder-day. For 800 books in 20 days, binders = 800 / (20 x 4.44) = 9.
12 men and 15 women can reap a field in 14 days. Find the days that 7 men and 5 women can take to reap it?
Solving the two rates shows a man and a woman work at the same speed here, so 12 + 15 = 27 workers take 14 days, a job of 378 worker-days. Then 7 + 5 = 12 workers take 378/12 = 31.5 days.
An army camp of 200 men has enough food for 60 days. How long will the food last if the number of men in the camp is reduced to 160?
The food is 200 x 60 = 12,000 man-days, so 160 men can be fed for 12,000/160 = 75 days.
If P*Q= P+Q+P/Q then 8*2 is?
8*2 = 8 + 2 + 8/2 = 10 + 4 = 14.
A ladder makes an angle of 60 degree with the ground against a wall. If the foot of ladder 2m away from the wall. The length of ladder is?
The foot of the ladder is the adjacent side, so cos(60) = 2/L. Since cos(60) = 0.5, L = 4 m.
Four People shared a taxi to the airport. The fare was Rs.40 and they gave the driver a tip 30% of the fare. If they equally shared the cost of fare and tip how much did each person pay?
The tip is 30% of 40 = 12, so the total is 52. Shared four ways that is 13 each.
If x-y=6 and x+y=16, then x is?
Adding x – y = 6 and x + y = 16 gives 2x = 22, so x = 11.
In a class of 33, the boys outnumber the girls by seven. How many girls are there?
If boys = girls + 7 and the total is 33, then 2g + 7 = 33, so g = 13 girls.
A trader mixes 26 kg of rice at Rs. 20 kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixed variety of rice at Rs. 30 per kg. What will be his profit percentage?
Cost = 26 x 20 + 30 x 36 = 520 + 1,080 = 1,600 for 56 kg. Selling at 30 gives 56 x 30 = 1,680. Profit = 80/1,600 = 5%.
If 2:7:: x: 49, then what is the value of “x”?
2 : 7 = x : 49 means x = 2 x 49 / 7 = 14.
The selling price of an article is Rs. 118 and the profit earned is 50%. The cost price of the article is?
A 50% profit means the selling price is 1.5 times cost, so cost = 118 / 1.5 = 78.67.
The cost price of 20 articles is the same as the selling price of X article. If the profit is 25% then the value of X is?
Cost of 20 = selling price of X, and selling price = 1.25 x cost each. So 20C = X(1.25C), giving X = 16.
A is the mother of B and C, D is the husband of C. What is the relation of A to D?
A is the mother of C, and D is married to C, so A is D's mother-in-law.
X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?
X does 1/20 per day and Y does 1/12. X alone for 4 days completes 1/5, leaving 4/5. Together they do 1/20 + 1/12 = 2/15 per day, taking (4/5)/(2/15) = 6 more days. The work lasted 4 + 6 = 10 days.
A candidate was selected for 6 jobs as he gave 15 interviews. What is the ratio of not selected jobs to the number of interviews?
Not selected = 15 – 6 = 9. The ratio to interviews is 9 : 15 = 3 : 5.
If a-b=3 and a^2+b^2=29, find the value of ab?
(a-b)^2 = a^2 – 2ab + b^2, so 9 = 29 – 2ab. Then 2ab = 20 and ab = 10.
A Company invited applications for 1,00,000 shares and it received applications for 1,50,000 shares. Applications for 30,000 shares were rejected and the remaining were allotted shares on pro-rata basis. How many shares an applicant for 3,000 shares will be allotted?
After rejecting 30,000, applications for 120,000 shares compete for 100,000, a ratio of 5/6. So an applicant for 3,000 receives 3,000 x 5/6 = 2,500 shares.
The ratio of length to the breadth of a rectangle is 3:2. Its area is 2400 sq.m. What is the length of the field?
Let the sides be 3k and 2k. Area = 6k^2 = 2,400, so k^2 = 400 and k = 20. The length is 3 x 20 = 60 m.
Solve 5+6×3-2+2?
Multiplication first: 6 x 3 = 18. Then 5 + 18 – 2 + 2 = 23.
If 3x+16=40, then find the value of “x”?
3x + 16 = 40 gives 3x = 24, so x = 8.
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?
Let the numbers be 3k and 5k. Then (3k+2)/(5k+2) = 2/3, giving 9k + 6 = 10k + 4, so k = 2 and b = 5 x 2 = 10.
Total number of students in a class in 2016 were 550. Their strength increased by 12%. What is the total strength now?
550 x 1.12 = 616.
Find the value of x. 31/12 = 20/x.
Cross-multiplying 31/12 = 20/x gives 31x = 240, so x = 240/31.
Four years ago, the average age of A, B, and C was 25 years. Five years ago, the average age of B and C was 20 years. What is the present age of A?
Four years ago A+B+C averaged 25, a total of 75, so today they total 75 + 12 = 87. Five years ago B+C totalled 40, so today they total 50. Therefore A = 87 – 50 = 37 years.
How many millimeters are there in one centimeter?
There are 10 millimetres in one centimetre.
Two numbers whose sum is 67 and difference is 3. Which of the following is one of the numbers?
The numbers are (67+3)/2 = 35 and (67-3)/2 = 32.
A shirt costs $20 and is reduced by 20%. How much will the new price be?
A 20% reduction leaves 80%: 20 x 0.8 = 16 dollars.
A car travels 240 km in 6 hours. If the speed of the car remains constant, how far will it travel in 9 hours?
The speed is 240/6 = 40 km/h, so in 9 hours the car travels 9 x 40 = 360 km.
The sum of three consecutive integers is 48. What is the smallest integer?
Three consecutive integers sum to 3n + 3 = 48, so n = 15.
If the average of 7 numbers is 40, what is the sum of the numbers?
Sum = 40 x 7 = 280.
The positive number which when multiplied by itself gives 422500 is?
650 x 650 = 422,500, so the number is 650.
In a group of 10 people, everyone shakes hands with each other once. How many handshakes will there be altogether?
Each handshake pairs two people, so the count is 10C2 = 10 x 9 / 2 = 45.
Haider made a profit of 25% in the first year. Next year he had a loss of 20% on the capital he had at the beginning of the second year. What was his overall loss or profit?
A 25% gain then a 20% loss gives 1.25 x 0.80 = 1.00, so he ends exactly where he started: neither profit nor loss.
Ali is twice as old as his youngest brother. If the difference between their ages is 15 years, how old is his youngest brother?
If the brother is b then Ali is 2b, and 2b – b = 15, so b = 15 years.
A is twice as good as B as a workman. A takes 30 days less than B to complete a work. How many days will both take to complete the work together?
If B takes t days then A takes t/2, and t – t/2 = 30 gives t = 60, so A takes 30. Together they do 1/60 + 1/30 = 1/20 per day, that is 20 days.
What is 45% of 225?
45% of 225 = 0.45 x 225 = 101.25.
10 men have ration for 21 days in the camp. If 3 men leave the camp, for how many days will the ration be sufficient for the remaining men?
The ration is 10 x 21 = 210 man-days. With 7 men remaining it lasts 210/7 = 30 days.
When you divide 0.7 by 10, you will get?
0.7 / 10 = 0.07.
After spending 88% of his income, a man had Rs. 2160 left. Find his income?
Spending 88% leaves 12%, so 0.12 x income = 2,160 and income = 18,000.
If A and B together can complete a job in 15 days and B alone can complete it in 20 days. In how many days can A alone complete the job?
A and B do 1/15 per day and B alone does 1/20, so A does 1/15 – 1/20 = 1/60, that is 60 days.
If 2x + 7 = 19, then x is?
2x + 7 = 19 gives 2x = 12, so x = 6.
A train 800-meter-long is running with a speed of 78 km/h. It crosses a tunnel in 1 minute. What is the length of the tunnel?
78 km/h = 21.67 m/s. In 60 seconds the train covers 1,300 m, which is the train plus the tunnel. So the tunnel is 1,300 – 800 = 500 m.
Find the average of the numbers: 277, 278, 279, 280, 281, 282, 283?
The numbers are consecutive and evenly spread, so the average is the middle value, 280.
About the PPSC Mathematics Past Paper 2020
Every MCQ above is taken from the Punjab Public Service Commission (PPSC) Mathematics papers held in 2020, 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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