PPSC Mathematics Past Paper 2024 Solved MCQs with Answers
Solved Mathematics MCQs from the PPSC 2024 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 2024 paper and verified before publication.
The numerator of a fraction is 4 less than the denominator. If 1 is added to both its numerator and denominator, it becomes 1/2. Find the fraction.
Let the fraction be n/(n+4). Adding 1 to both parts gives (n+1)/(n+5) = 1/2, so 2n + 2 = n + 5 and n = 3. The fraction is 3/7.
A washerman irons 4 shirts in 12 minutes. How many shirts can he iron in one hour?
4 shirts take 12 minutes, so the rate is 1 shirt every 3 minutes. In 60 minutes he irons 60/3 = 20 shirts.
The angle of depression of a point situated at a distance of 70m from the base of a tower is 60°. The height of the tower is?
height = distance x tan(60) = 70 x sqrt3 = 70 sqrt3 metres.
The sum of ages of two children is 12 and their product is 32. What is the age of the elder child?
Two numbers with sum 12 and product 32 are 4 and 8, since 4 + 8 = 12 and 4 x 8 = 32. The elder child is 8.
Four men working together can dig a ditch in 42 days. They begin, but one man works only half-days. How long will it take to complete the job?
Four men need 4 x 42 = 168 man-days. With one man on half days the daily effort is 3.5 men, so the time is 168 / 3.5 = 48 days.
Saleem bought a car for Rs. 875,000 and paid 17% as GST. How much tax did he pay?
GST = 17% of 875,000 = 0.17 x 875,000 = 148,750.
The sum of two numbers is 10 and their product is 20. What is the sum of their reciprocals?
The sum of reciprocals is (a + b)/(ab) = 10/20 = 1/2.
If a certain job can be finished by 18 workers in 26 days. How many workers are needed to finish the job in 12 days?
The job needs 18 x 26 = 468 worker-days. To finish in 12 days requires 468 / 12 = 39 workers.
Which term of the AP 2, 11, 20, 29… is 290?
For the A.P. 2, 11, 20, … a = 2 and d = 9. Setting 2 + 9(n-1) = 290 gives 9(n-1) = 288, so n – 1 = 32 and n = 33.
Amy buys 'd' dollars' worth of groceries each week and spends one fourth of those dollars on fruit. In terms of 'd', how many weeks will it take Amy to spend a total of $100 just on fruit?
Amy spends d/4 on fruit each week. To reach 100 she needs 100 / (d/4) = 400/d weeks.
In an examination, 80% of candidates passed in English, and 85% of candidates passed in Mathematics. If 73% of candidates passed in both subjects, then what percentage of candidates failed in both subjects?
Passed at least one subject = 80 + 85 – 73 = 92%. So those who failed both = 100 – 92 = 8%.
A flagstaff 17.5 m high casts a shadow of length 40.25 m. The height of the building which casts a shadow of length 28.75 m under similar conditions will be?
Shadows are proportional to heights: 17.5 / 40.25 = h / 28.75. So h = 17.5 x 28.75 / 40.25 = 12.5 m.
Find the correct value of x: 3889 + 12.952 – x = 3854.002
3889 + 12.952 = 3901.952. Then x = 3901.952 – 3854.002 = 47.95.
4.036 divided by 0.04 gives?
4.036 / 0.04 = 403.6 / 4 = 100.9.
Roshan bought 5 pants at Rs 25 each, 10 shirts at Rs 50 each, and 15 ties at Rs 35 each. Find the average price of all the articles.
Total cost = 5(25) + 10(50) + 15(35) = 125 + 500 + 525 = 1,150 for 30 articles. Average = 1150/30 = 38.33.
The average speed of a car is 75 km/h. The driver first decreases its average speed by 40% and then increases it by 50%. What is the new average speed now?
Decreasing 75 by 40% gives 75 x 0.6 = 45. Increasing that by 50% gives 45 x 1.5 = 67.5 km/h.
Three persons A, B and C spend 80%, 85% and 75% of their salaries respectively. The sum of their salaries is Rs. 72,000 and their savings are in the ratio 8: 9: 20. What is the salary of A?
They save 20%, 15% and 25% of salary, in the ratio 8 : 9 : 20. So 0.20A = 8k gives A = 40k, 0.15B = 9k gives B = 60k, and 0.25C = 20k gives C = 80k. Total 180k = 72,000, so k = 400 and A = 16,000.
The sum of three consecutive even natural numbers is 78. Find the greatest of these numbers.
Three consecutive even numbers summing to 78 are 24, 26 and 28. The greatest is 28.
An observer 1.6m tall is 20√3m away from a tower. The angle of elevation from his eye to the top of the tower is 30°. The height of the tower is?
The height above eye level = 20sqrt3 x tan(30) = 20sqrt3 / sqrt3 = 20 m. Adding the observer's height gives 20 + 1.6 = 21.6 m.
Waleed gave 25% of a profit to his partner. If the partner got Rs. 8000, what remains with Waleed?
25% of the profit is 8,000, so the whole profit is 32,000. Waleed keeps 32,000 – 8,000 = 24,000.
The area of a circle is 275 cm². What is the circumference of the circle?
Area = pi r^2 = 275, so r = sqrt(275/pi) = 9.355 cm. Circumference = 2 pi r = 58.79 cm.
An ornament seller marks the price of an article at Rs. 28,800. Find the selling price of the article if he gives a discount of 20%.
A 20% discount leaves 80% of the marked price: 28,800 x 0.8 = 23,040.
The sum of the squares of two numbers is 97 and the square of their difference is 25. The product of the two numbers is?
(a – b)^2 = a^2 + b^2 – 2ab, so 25 = 97 – 2ab. Therefore 2ab = 72 and ab = 36.
If Ali’s salary is 10% more than that of Sajjad’s, then how much percent is Sajjad’s salary less than that of Ali?
If Sajjad earns 100, Ali earns 110. Sajjad is 10 less out of Ali's 110, that is 10/110 = 1/11, which is 100/11 per cent.
How many pieces of 13.2 cm can be cut from a 330 cm long rod?
330 / 13.2 = 25 pieces.
If one angle of a parallelogram is 24° less than twice the smallest angle, then the largest angle of the parallelogram is?
Let the smallest angle be x. The other is 2x – 24. Adjacent angles of a parallelogram add to 180, so x + 2x – 24 = 180, giving x = 68. The largest angle is 2(68) – 24 = 112 degrees.
What will be the ratio of simple interest earned by a certain amount at the same rate of interest for 12 years and for 18 years?
Simple interest is proportional to time, so the ratio for 12 and 18 years is 12 : 18 = 2 : 3.
On a 20% discount sale, an article costs 596. What was the original price of the article?
After a 20% discount the price is 80% of the original, so original = 596 / 0.8 = 745.
If 6 persons working 8 hours a day earn Rs.8400 per week, then how much will 9 persons be working 6 hours a day each per week?
6 persons x 8 hours = 48 person-hours earn 8,400, that is 175 per person-hour. 9 persons x 6 hours = 54 person-hours, earning 54 x 175 = 9,450.
If a person pays Zakat as Rs. 8500, what is the total amount of their wealth?
Zakat is 2.5% of wealth, so wealth = 8,500 / 0.025 = 340,000.
Find the maximum number of students among whom 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and the same number of pencils?
The number of students must divide both totals, so take the HCF. 1001 = 7 x 11 x 13 and 910 = 2 x 5 x 7 x 13, giving HCF = 7 x 13 = 91.
The sum of two numbers is 45. 4 times the first number is 9 less than 5 times the second, what are the two numbers?
x + y = 45 and 4x = 5y – 9. Substituting x = 45 – y gives 180 – 4y = 5y – 9, so 9y = 189 and y = 21, x = 24.
A can do a piece of work in 4 days and B can do it in 12 days. In how many days will they finish the work, both working together?
A does 1/4 per day and B does 1/12 per day. Together 1/4 + 1/12 = 1/3 per day, so 3 days.
What is 70 percent of 900?
70% of 900 = 0.70 x 900 = 630.
In a regular 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?
Exterior and interior angles add to 180 and are in the ratio 2 : 13, so the exterior angle is 180 x 2/15 = 24 degrees. Number of sides = 360/24 = 15.
Two concentric circles are of radii 10 cm and 6 cm. Find the length of the chord of the larger circle which touches the smaller circle?
The chord touching the inner circle is bisected at the point of contact, forming a right triangle with sides 6 and 10. Half the chord = sqrt(100 – 36) = 8, so the chord is 16 cm.
A polygon having four sides is called?
A polygon with four sides is a quadrilateral.
What is the result of the Excel formula (7-3)x(4+3)/4?
(7 – 3) x (4 + 3) / 4 = 4 x 7 / 4 = 7.
If the cost of tiles is Rs.5 for 50 sq.m, what will be the cost of 400 sq.m?
400 sq.m is 8 times 50 sq.m, so the cost is 8 x 5 = 40 rupees.
A train covers 32 kilometers in 14.5 minutes. If it continues to travel at the same rate, which of the following is closest to the distance it will travel in 2 hours?
In 2 hours, that is 120 minutes, distance = 32 x 120 / 14.5 = 264.8, closest to 265 kilometres.
What is the product of -2, -3 and -10?
(-2) x (-3) = 6, and 6 x (-10) = -60.
The measures of the angles of a triangle are in the ratio 5:4:3. Find the smallest angle of triangle?
The ratio 5 : 4 : 3 has 12 parts for 180 degrees, so one part is 15 degrees. The smallest angle is 3 x 15 = 45 degrees.
The average of the first 100 natural number is?
The average of the first n natural numbers is (n+1)/2. For n = 100 that is 101/2 = 50.5.
The population of a certain village is 62500. What will be its population after 3 years if it increases geometrically at the rate of 4% annually?
Population = 62,500 x (1.04)^3 = 62,500 x 1.124864 = 70,304.
If 5 men take an hour to dig a ditch, how long should it take for 12 men to dig a ditch of the same type?
5 men take 60 minutes, so the job is 300 man-minutes. With 12 men it takes 300/12 = 25 minutes.
378 trees are planted in rows in the shape of an isosceles triangle, the numbers in successive rows decreasing by one from the base to the top. How many trees are there in the row which forms the base of the triangle?
Rows decreasing by one form 1 + 2 + … + n = n(n+1)/2 = 378. Solving n^2 + n – 756 = 0 gives n = 27, so the base row has 27 trees.
The average weight of 7 people is 70 kg. If one person weighing 80 kg is replaced by a person weighing 60 kg, what will be the new average weight?
Replacing an 80 kg person with a 60 kg person reduces the total by 20 kg. New total = 490 – 20 = 470, so the average is 470/7 = 67.14 kg.
If a machine makes 4 yards of cloth in two minutes. How many yards of cloth will the machine make in 50 minutes?
The machine makes 2 yards per minute, so in 50 minutes it makes 100 yards.
The difference between two numbers is 18. If 4 times the second number is less than three times the first number by 18, what is the sum of these two numbers is?
a – b = 18 and 3a – 4b = 18. Substituting a = b + 18 gives 3b + 54 – 4b = 18, so b = 36 and a = 54. Their sum is 90.
If an 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?
20 : 16 divides by 4 to give 5 : 4.
In the sequence 35, 45, 55, … what is the 10th term?
The sequence 35, 45, 55 has a = 35 and d = 10. The 10th term = 35 + 9(10) = 125.
A train travels 16 km in 20 minutes. The speed of the train is?
16 km in 20 minutes is 16 x 3 = 48 km in 60 minutes, so 48 km/h.
The distance between two cities is 203 miles, and the journey takes 3 1/2 hours. What is the average speed of the vehicle?
Speed = 203 / 3.5 = 58 miles per hour.
The sum of two numbers is 138, and their difference is 68. What is the smallest number?
The smaller number = (sum – difference)/2 = (138 – 68)/2 = 35.
A pile of 108 identical books weight 30 kg. How many books weight 40 kg?
108 books weigh 30 kg, so 40 kg holds 108 x 40/30 = 144 books.
A car travels a distance of 510 km in 6 hours. What is the average speed of the car?
Average speed = 510 / 6 = 85 km/h.
The product of 0.003×0.02?
0.003 x 0.02 = 0.00006.
What is the 15th term of the sequence 20, 15, 10…?
The sequence 20, 15, 10 has d = -5. The 15th term = 20 + 14(-5) = 20 – 70 = -50.
The ratio of 8 inch to 7 feet will be?
7 feet = 84 inches. The ratio 8 : 84 divides by 4 to give 2 : 21.
A student has obtained 75%, 80%, and 85% in three subjects. If the marks of another subject are added, his average can’t be less than 80%. What are the minimum marks required in the fourth subject?
For an average of at least 80 over four subjects the total must be at least 320. The first three give 75 + 80 + 85 = 240, so the fourth must be at least 80%.
One fifth of the sum of two angles is 24 degree and half of their difference is 14 degree. Calculate the largest angle?
One fifth of the sum is 24, so the sum is 120. Half the difference is 14, so the difference is 28. The larger angle = (120 + 28)/2 = 74 degrees.
If x: y = 2:1, then (5x² – 13xy + 6y²) is equal to?
With x = 2y, the expression becomes 5(4y^2) – 13(2y)(y) + 6y^2 = 20y^2 – 26y^2 + 6y^2 = 0.
A volleyball team won 5 matches, which accounts for 25% of the total matches they played. Determine the total number of matches they participated?
5 matches are 25% of the total, so the total = 5 / 0.25 = 20 matches.
If 7/21 of a number is 6, what is 14/21 of that number?
7/21 is 1/3, so one third of the number is 6 and the number is 18. Then 14/21 is 2/3, giving 12.
If 80% of the applicants to a program were rejected, what is the ratio of the number accepted to the number rejected?
If 80% were rejected then 20% were accepted, so accepted : rejected = 20 : 80 = 1 : 4.
Find the breadth of a rectangular field whose length is 18 m and area is 216 m²?
Breadth = area / length = 216 / 18 = 12 m.
The ratio between two numbers is 3:4. If each number is increased by 3, the ratio becomes 4:5. Find the difference between the numbers?
Let the numbers be 3k and 4k. Then (3k+3)/(4k+3) = 4/5, so 15k + 15 = 16k + 12 and k = 3. The numbers are 9 and 12, differing by 3.
If 3x + (3/4)x = 5/4, what is the value of x?
3x + (3/4)x = (15/4)x = 5/4. Therefore x = (5/4) x (4/15) = 1/3.
Find the breadth of a rectangular field, given that its length is 18 meters and its area is 666 square meters?
Breadth = area / length = 666 / 18 = 37 m.
If the mean of 7 terms is 40, the sum of those terms will be?
Sum = mean x number of terms = 40 x 7 = 280.
A train covers a distance in 5 hours at 45 km/h. What speed is required to cover the same distance in 3 hours?
The distance is 5 x 45 = 225 km. To cover it in 3 hours needs 225/3 = 75 km/h.
A car wash can wash 8 cars in 18 minutes, at this rate, how many cars can be wash in 3 hours?
8 cars take 18 minutes, so in 180 minutes the wash handles 8 x 10 = 80 cars.
A die is rolled twice. Find the probability that 5 will come up both the times?
Each roll gives a 5 with probability 1/6, and the rolls are independent, so 1/6 x 1/6 = 1/36.
In an examination 25% candidates failed in Mathematics and 20% students failed in English. If 5% students failed in both the subjects, find percentage of students who passed in both subjects?
Failed at least one subject = 25 + 20 – 5 = 40%. So those who passed both = 100 – 40 = 60%.
The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is?
If the larger is 15 times the smaller, then 15y^2 = 9375, so y^2 = 625 and y = 25. The larger is 375, and the sum is 400.
If 8 men or 12 women can do a piece of work in 25 days, in how many days can the same work be done by 6 men and 11 women?
8 men equal 12 women, so 1 man equals 1.5 women. Then 6 men and 11 women equal 9 + 11 = 20 women. Since 12 women take 25 days, 20 women take 12 x 25 / 20 = 15 days.
What is the ratio of 12 minute to 1 hour?
12 minutes to 60 minutes is 12 : 60 = 1 : 5.
If the number of elements in set A is 20, in set B is 30, and the number of elements in the union of sets A and B is 40, what is the number of elements in the intersection of sets A & B?
Using n(A union B) = n(A) + n(B) – n(A intersect B), we get 40 = 20 + 30 – x, so x = 10.
A man bought a piece of land worth Rs. 300,000 and sold it for 240,000. What is his loss percentage?
Loss = 300,000 – 240,000 = 60,000. Loss percentage = 60,000 / 300,000 x 100 = 20%.
A therapist is preparing a poster that will clarify some of the data in an in service presentation. The poster reflects the mode, median, and mean of a set of data. The data consist of the numbers 2, 2, 4, 9, and 13. If presented in the above order (mode, median mean), which of the following is the correct list of answers calculated from the data?
For 2, 2, 4, 9, 13 the mode is 2 (most frequent), the median is 4 (middle value), and the mean is 30/5 = 6. In order that is 2, 4, 6.
A number is doubled and 9 is added. If the result is tripled it becomes 75. What is that number?
Let the number be n. Then 3(2n + 9) = 75, so 2n + 9 = 25 and n = 8.
An internet service provider charges a onetime setup fee of $100 and $50 each month for service. If c customers join at the same time and are on the service for m months, which of the following expressions represents the total amount, in dollars, the provider has charged these customers?
Each customer pays 100 once plus 50 for each of m months, that is 100 + 50m. For c customers the total is 100c + 50cm.
Find the odd one out: 140, 340, 540, 730, 940, 1140?
The numbers rise by 200 each time: 140, 340, 540, 740, 940, 1140. The value 730 breaks the pattern and is the odd one out.
Umar paid Rs.7895 as tax at 10% of the total amount he earned. What was the total amount he earned?
The tax is 10% of earnings, so earnings = 7,895 / 0.10 = 78,950.
The cost of an article was Rs.75. The cost was first increased by 20% and later on it was reduced by 20%. The present cost of the article is?
Increasing 75 by 20% gives 90. Reducing 90 by 20% gives 90 x 0.8 = 72. Note the result is below the original, since the second percentage applies to a larger base.
If m:n=3:2, then (4m + 5n): (4m – 5n) is equal to?
Let m = 3k and n = 2k. Then (12k + 10k) : (12k – 10k) = 22k : 2k = 11 : 1.
Find the 4th proportional to 4, 16 and 7?
The fourth proportional satisfies 4 : 16 = 7 : x, so x = 16 x 7 / 4 = 28.
If a person deposits 5,000 in the first month, 10,000 in the second month, and 15,000 in the third month, how much money will they deposit in the ninth month?
The deposits form an A.P. with a = 5,000 and d = 5,000, so the ninth month is 9 x 5,000 = 45,000.
How many bricks each of volume 750 cm³ will be required to construct a wall 10m long, 5m wide, and 30cm high?
Wall volume = 1000 x 500 x 30 = 15,000,000 cubic cm. Dividing by 750 gives 20,000 bricks.
Find interest on Rs. 40,000 at the rate of 3% annually for 4 years investment?
SI = P x R x T / 100 = 40,000 x 3 x 4 / 100 = 4,800.
The average of 5 numbers is 42. If we include a sixth number, 48, then the new average will be?
The five numbers total 5 x 42 = 210. Adding 48 gives 258 over six numbers, so the new average is 258/6 = 43.
The average height of a class of 25 students is 4.4 feet. A student of height 5.7 feet is newly enrolled. Find the new average?
25 students total 25 x 4.4 = 110 feet. Adding 5.7 gives 115.7 over 26 students, so the average is 4.45 feet.
The square root of 6084 is?
78 x 78 = 6,084, so the square root of 6,084 is 78.
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?
The ages 3k, 5k and 7k total 15k, and the average is 15, so 15k = 45 and k = 3. The youngest is 3 x 3 = 9 years.
What is the fifth term of the geometric sequence whose first term is 3 and whose common ratio is 2?
The fifth term of a geometric sequence = a r^4 = 3 x 2^4 = 3 x 16 = 48.
About the PPSC Mathematics Past Paper 2024
Every MCQ above is taken from the Punjab Public Service Commission (PPSC) Mathematics papers held in 2024, 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.
How to Use This Paper
Attempt the full quiz before looking at any answer, then read the explanation for every question you got wrong, including those you guessed correctly. A past paper is only useful if you close the gaps it exposes. Pro members can download the complete paper as a PDF with all answers and explanations for offline revision.