PPSC Mathematics Past Paper 2025 Solved MCQs with Answers
Solved Mathematics MCQs from the PPSC 2025 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 2025 paper and verified before publication.
380 is 40% of which value?
Let the value be x. Then 40% of x = 380, so 0.4x = 380 and x = 380 / 0.4 = 950.
Which is next term in given sequence? 5,11,19,29,—?
The differences are 6, 8, 10, increasing by 2 each time. The next difference is 12, so the next term is 29 + 12 = 41.
How many solutions of given pair of equation 3x-6y=15 and -2x+4y=-10?
Multiply the first equation by 2 and the second by 3: 6x – 12y = 30 and -6x + 12y = -30. These are the same line, so the system has infinitely many solutions.
If 3rd term of A.P is 8 and 6th term of A.P is 17. Find the 8th term of A.P?
For an A.P., a3 = a + 2d = 8 and a6 = a + 5d = 17. Subtracting gives 3d = 9, so d = 3 and a = 2. Then a8 = a + 7d = 2 + 21 = 23.
If 2√(x+2) = 3√2. Find the value of x?
Divide both sides by 2: sqrt(x+2) = 1.5 sqrt(2). Squaring gives x + 2 = 2.25 x 2 = 4.5, so x = 2.5.
If a person has $1.50, $6.05, and $3.25, what will be their total amount?
Add the three amounts: 1.50 + 6.05 + 3.25 = 10.80 dollars.
A bank teller uses the equation Y=1.30x-1.50 to exchange U.S. dollars into euros, where y is the euro amount and x is the U.S. dollar amount. Which of the following is the best interpretation of the 1.50 in the equation?
In y = 1.30x – 1.50, the 1.30 is the exchange rate per dollar and the constant 1.50 is subtracted whatever the amount exchanged. A fixed deduction of this kind is a flat fee, so the bank charges 1.50 euros.
If the simple interest is Rs. 54,000 at the rate of 12% per annum for 3 years, find the principal amount?
Simple interest P = (SI x 100) / (R x T) = (54000 x 100) / (12 x 3) = 5400000 / 36 = 150,000.
Find the positive value of (x) from equation: 4x^2-6x-4=0?
Divide through by 2: 2x^2 – 3x – 2 = 0. Factorising gives (2x + 1)(x – 2) = 0, so x = -1/2 or x = 2. The positive value is 2.
Simplify the ratio: 1 hour : 30 minutes : 45 seconds?
Convert to seconds: 3600 : 1800 : 45. Divide each by 45 to get 80 : 40 : 1.
Frequency is inversely proportional to wavelength. If the frequency of a wave with 3000m wavelength is 100 kHz, then what is the frequency of a wave with 500m wavelength?
Since frequency is inversely proportional to wavelength, f1 x L1 = f2 x L2. So 100 x 3000 = f2 x 500, giving f2 = 600 kHz.
An Aeroplane has to cover a journey of 600 km. Its original speed was 200 km/h. What was the original time of the journey?
Time = distance / speed = 600 / 200 = 3 hours.
The ratio of three numbers is 1:2 :3 and their product is 750. What is the largest number?
Let the numbers be x, 2x and 3x. Their product is 6x^3 = 750, so x^3 = 125 and x = 5. The largest number is 3x = 15.
What is the formula for the sum of the first n squares (1^2 + 2^2 + 3^2 + … + n^2)?
The sum of the first n squares is n(n+1)(2n+1)/6. For example with n = 3 it gives 3 x 4 x 7 / 6 = 14, which matches 1 + 4 + 9.
What is 20% more than 80,000?
20% more than 80,000 means 80,000 x 1.20 = 96,000.
Evaluate: 13.133 + 16.007 – 9.1320?
13.133 + 16.007 = 29.140, and 29.140 – 9.132 = 20.008.
The average monthly income of A&B is 50,500. The average monthly income of B&C is 62,500 and the average monthly income of A&C is 52,000. What is monthly income of A?
A + B = 101,000, B + C = 125,000 and A + C = 104,000. Adding all three gives 2(A + B + C) = 330,000, so A + B + C = 165,000. Then A = 165,000 – (B + C) = 165,000 – 125,000 = 40,000.
A rectangular metal block measuring 24cm x 19 cm x 15 cm is melted and recast into a cube. What is the length of each side of the cube (in cm)?
Volume of the block = 24 x 19 x 15 = 6,840 cubic cm. The cube has the same volume, so its side is the cube root of 6,840, which is about 18.98, that is 19 cm.
Solve: 16 × 5 – 2 + (84 – 3) + 37?
Working left to right with brackets first: 16 x 5 = 80; 80 – 2 = 78; (84 – 3) = 81. Then 78 + 81 + 37 = 196.
What is the sum of exterior angles of any polygon?
The sum of the exterior angles of any polygon is always 360 degrees, whatever the number of sides.
How many square feet are in one acre?
One acre equals 43,560 square feet.
A ball is dropped from a height of 75m. After each fall, it rebounds 2/5 of the distance it fell. What total distance does the ball travel before coming to rest?
The ball falls 75 m, then rises and falls 2/5 of each previous drop. Total = 75 + 2 x 75 x (2/5) / (1 – 2/5) = 75 + 2 x 75 x 0.4 / 0.6 = 75 + 100 = 175 m.
If 2x-7 = 8+x find the value of X?
2x – 7 = 8 + x. Subtract x from both sides: x – 7 = 8, so x = 15.
A clock strikes once at 1 o'clock, twice at 2 o'clock, and so on. How many times does it strike in 12 hours?
The clock strikes 1 + 2 + 3 + … + 12 times. Using n(n+1)/2 with n = 12 gives 12 x 13 / 2 = 78.
If each interior angle of a regular polygon is 162°, calculate the number of sides?
Each exterior angle = 180 – 162 = 18 degrees. Number of sides = 360 / 18 = 20.
If the principal amount is Rs. 15580, interest rate is 5% for a year and a half. Calculate the simple interest?
SI = P x R x T / 100 = 15,580 x 5 x 1.5 / 100 = 1,168.50.
If a man were to sell his chair for Rs. 720, he would lose 25%. To gain 25%, he should sell it for?
Selling at 720 gives a 25% loss, so cost price = 720 / 0.75 = 960. To gain 25%, sell at 960 x 1.25 = 1,200.
If log₂(x) = 5 what is the value of x?
log base 2 of x = 5 means x = 2^5 = 32.
If (sinθ+cosθ)/(sinθ-cosθ)=4/5 then (tan²θ+1)/(tan²θ-1)?
Divide numerator and denominator by cos to get (tan + 1)/(tan – 1) = 4/5. Cross-multiplying: 5tan + 5 = 4tan – 4, so tan = -9. Then (tan^2 + 1)/(tan^2 – 1) = (81 + 1)/(81 – 1) = 82/80 = 41/40.
If y=(x+1)(x+6), then its graph will intercept the y-axis how many times?
A graph meets the y-axis where x = 0, which gives exactly one value of y for a function. So it intercepts the y-axis once, at y = 1 x 6 = 6.
Find the missing term: 6:x::60:120, find x?
The proportion 6 : x :: 60 : 120 means 6/x = 60/120 = 1/2. So x = 12.
A parallelogram has sides 15 cm and 10 cm. Find its perimeter.
A parallelogram has opposite sides equal, so the perimeter is 2 x (15 + 10) = 50 cm.
Veronica has a bank account that offers m% interest compounded annually. If she opens the account with 200S, the expression 200S(X)^t represents the amount in the account after t years. Which of the following gives X in terms of m?
Compound interest gives amount = P(1 + r)^t where r is the rate as a decimal. Here the rate is m%, that is m/100 = 0.01m, so X = 1 + 0.01m.
Express 2log(x+1) + 3log(x+3) – log((x+1)^2) as a single logarithm log(Y). What is Y?
2log(x+1) = log((x+1)^2) and 3log(x+3) = log((x+3)^3). The log((x+1)^2) terms cancel, leaving log((x+3)^3), so Y = (x+3)^3.
The area of an equilateral triangle is √243/16. Find the length of a side of the triangle.
Area of an equilateral triangle = (sqrt3 / 4) a^2. Note sqrt243 = 9 sqrt3, so the area is 9sqrt3/16. Setting (sqrt3/4) a^2 = 9sqrt3/16 gives a^2 = 9/4 and a = 3/2.
Convert 90 km/h into cm/min.
90 km/h = 90,000 m/h = 9,000,000 cm/h. Dividing by 60 gives 150,000 cm per minute.
Given the system of equations: x+y=13 and x-y=1. What is the solution set (x, y)?
Adding the equations gives 2x = 14, so x = 7. Substituting back, y = 13 – 7 = 6. The solution is (7, 6).
40 men complete one-third of a work in 40 days. How many more men should be employed to finish the rest of the work in 50 more days?
40 men do one third in 40 days, so the whole job needs 40 x 40 x 3 = 4,800 man-days. The remaining two thirds needs 3,200 man-days in 50 days, that is 64 men. Since 40 are already working, 24 more are needed.
A circular wheel has a diameter of 30cm. The wheel rolls a distance of 150m. Calculate the number of complete revolutions.
Circumference = pi x 30 = 94.25 cm. The distance is 150 m = 15,000 cm. 15,000 / 94.25 = 159.2, so 159 complete revolutions.
A train travels 240km with uniform speed. If the speed of the train increased by 4km/hour, it takes 0.5 hours less to cover the same journey. Find the original speed of the train.
Let the speed be v. Then 240/v – 240/(v+4) = 0.5, which simplifies to v^2 + 4v – 1920 = 0. Solving gives v approximately 41.9, so the original speed is 42 km/h.
Find the value of m that makes the points P(1, 2), Q(4, m), and R(5, 4) collinear.
Points are collinear when the slopes match. Slope PR = (4 – 2)/(5 – 1) = 1/2. Slope PQ = (m – 2)/(4 – 1) = 1/2, so m – 2 = 3/2 and m = 7/2.
An army formation of 900 men has a food stock for 30 days. On some days 150 army men leave the formation. For how many days will the food be sufficient for the remaining men?
The food is 900 x 30 = 27,000 man-days. With 150 men leaving, 750 remain, so the food lasts 27,000 / 750 = 36 days.
Two poles are in a straight position with lengths 5m and 12m. The distance between their bases is 7m. Find the distance between their tops.
The tops differ in height by 12 – 5 = 7 m, and the bases are 7 m apart. By Pythagoras the distance between the tops is sqrt(7^2 + 7^2) = 7 sqrt2 m.
If a girl jumps 820 times in 1 hour, how many times will she jump in 30 minutes?
30 minutes is half an hour, so she jumps 820 / 2 = 410 times.
The value of sin 90° x cos 90°?
sin 90 = 1 and cos 90 = 0, so the product is 1 x 0 = 0.
If ABCD is a square with given points A(2,3), B(-2,2), C(-1,-2), then what are the coordinates of D?
In a square ABCD the diagonals bisect each other, so D = A + C – B. That gives (2 + (-1) – (-2), 3 + (-2) – 2) = (3, -1).
If 78 students represent 30% of the total class strength, the total number of students in the class?
78 students are 30% of the class, so the total = 78 / 0.30 = 260.
The sum of 0.3 + 0.03 + 0.003 + 0.0003?
Adding place by place: 0.3 + 0.03 + 0.003 + 0.0003 = 0.3333.
The additive inverse of -5 is?
The additive inverse of a number is what you add to it to get zero. For -5 that is 5.
If 1/5 of the keyboards are not working out of a total of 3,000, how many keyboards are working?
If one fifth are not working, four fifths are working: 3,000 x 4/5 = 2,400.
If the principal amount is $1000, the rate of interest is 2% per year, and the time period is 3 years, what is the simple interest?
SI = P x R x T / 100 = 1000 x 2 x 3 / 100 = 60 dollars.
What is the simplified ratio of 2 km to 400 meters?
2 km = 2,000 m. The ratio 2,000 : 400 divides by 400 to give 5 : 1.
The angle of elevation of the top of a tower from a point 20 m away from its base is 45°. What is the height of the tower?
tan 45 = height / 20, and tan 45 = 1, so the height equals the distance, 20 m.
If y is directly proportional to x², and when x is 2, y is 20, what is the value of y when x is 3?
y = kx^2. When x = 2, y = 20, so 20 = 4k and k = 5. When x = 3, y = 5 x 9 = 45.
Three years ago, the average age of a family of 5 members was 17 years. A baby having been born and the average age of the family is the same as three years ago. The present age of the baby (in years) is?
Three years ago 5 members averaged 17, a total of 85. Today those five total 85 + (5 x 3) = 100. The family of 6 still averages 17, a total of 102. So the baby is 102 – 100 = 2 years old.
If the side of a square is 5 units, what is its area?
Area of a square = side^2 = 5^2 = 25 square units.
A and B finish a job in 12 days. While A, B, and C together can finish it in 8 days. How many days will it take for C alone to finish the job?
A and B do 1/12 of the job per day, and A, B and C do 1/8 per day. So C alone does 1/8 – 1/12 = 1/24 per day, taking 24 days.
44^7 * 44^x = 1, then the value of x is?
44^7 x 44^x = 44^(7+x) = 1 = 44^0. So 7 + x = 0 and x = -7.
How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
SI = P x R x T / 100, so 81 = 450 x 4.5 x T / 100 = 20.25T. Therefore T = 4 years.
What is the result of the following expression: 5 + 51 + (-3) + 7 + (-5.1)?
5 + 51 – 3 + 7 – 5.1 = 63 – 8.1 = 54.9.
If X = 80% of Y and Z = 120% of X, then the ratio X: Y: Z will be?
Take Y = 100. Then X = 80 and Z = 1.2 x 80 = 96. So X : Y : Z = 80 : 100 : 96, which simplifies to 20 : 25 : 24.
A number multiplied by 3/4 of itself gives 10800. What is the number?
Let the number be n. Then n x (3/4)n = 10,800, so (3/4)n^2 = 10,800 and n^2 = 14,400, giving n = 120.
A cube has an edge of 18 cm. How many smaller cubes of edge 3 cm can be cut from it?
Volume of the big cube = 18^3 = 5,832. Each small cube is 3^3 = 27. So 5,832 / 27 = 216 small cubes.
What is the sum of mn + 4 – 3 and -2mn + 3?
(mn + 4 – 3) + (-2mn + 3) = mn + 1 – 2mn + 3 = -mn + 4.
Find LCM of 27 & 63?
27 = 3^3 and 63 = 3^2 x 7. The LCM takes the highest power of each factor: 3^3 x 7 = 189.
An article is sold for 596 after a 20% discount. What was the original price?
After a 20% discount the price is 80% of the original, so original = 596 / 0.8 = 745.
The sum of the ages of a son and a father is 64. After 4 years the age of father will be three times that of his sons. The age of the father is?
Let the son be s and the father f, with s + f = 64. In 4 years f + 4 = 3(s + 4), so f = 3s + 8. Then s + 3s + 8 = 64, giving s = 14 and f = 50.
What is 17% GST on 1,087,500?
17% of 1,087,500 = 0.17 x 1,087,500 = 184,875.
2x-5y=a; bx+10y=-8 In the system of equations above, a and b are constants. If the system has infinitely many solutions, what is the value of a?
For infinitely many solutions the equations must be proportional. Comparing the y terms, 10 / -5 = -2, so multiply the first equation by -2: -4x + 10y = -2a. Matching with bx + 10y = -8 gives b = -4 and -2a = -8, so a = 4.
Given f(x) =3x²+2x+4 what is the value of f (3)?
f(3) = 3(9) + 2(3) + 4 = 27 + 6 + 4 = 37.
A person's income increased from Rs. 7,800 to Rs. 10,500 in 3 years. What is the percentage increase in income?
Increase = 10,500 – 7,800 = 2,700. Percentage increase = 2,700 / 7,800 x 100 = 34.62%.
Simplify the expression: 27+|2|+|-2|- 22?
The absolute values give |2| = 2 and |-2| = 2. So 27 + 2 + 2 – 22 = 9.
The area of a rectangular field is 17 m by 13 m. If the cost of tiling is 70 per square meter, what is the total cost of tiling the field?
Area = 17 x 13 = 221 square metres. Cost = 221 x 70 = 15,470.
If 54 is subtracted from 3 times a certain number, the result is 36. What is the number?
3n – 54 = 36, so 3n = 90 and n = 30.
A pupil’s marks were wrongly entered as 83 instead of 63. Due to this, the average marks for the class increased by half. The number of pupils in the class is?
The entered mark was 20 too high. Spreading 20 over n pupils raised the average by 0.5, so 20/n = 0.5 and n = 40.
If (x-y)²=44 and xy=22, what is the value of x²+y²?
(x – y)^2 = x^2 – 2xy + y^2 = 44. Since xy = 22, x^2 + y^2 = 44 + 2(22) = 88.
A coach was scheduled to depart at 22:55 and arrive at 06:05 the next day. What was the duration of the journey?
From 22:55 to midnight is 1 hour 5 minutes, and from midnight to 06:05 is 6 hours 5 minutes. Total = 7 hours 10 minutes.
If A:B=2:3 and B:C=4:7, and the total amount is 410,000, what is B’s share?
Make B common: A : B = 2 : 3 = 8 : 12, and B : C = 4 : 7 = 12 : 21. So A : B : C = 8 : 12 : 21, totalling 41 parts. B's share = 410,000 x 12/41 = 120,000.
The sum of three consecutive integers is 33. Find the smallest integer?
Let the integers be n, n+1, n+2. Their sum 3n + 3 = 33, so n = 10. The smallest is 10.
A mobile phone costs Rs. 64,800 after including 8% GST. What is the original price before tax?
The price including 8% GST is 1.08 times the original, so original = 64,800 / 1.08 = 60,000.
If 1 is added to the largest four-digit number, the number becomes?
The largest four-digit number is 9,999. Adding 1 gives 10,000.
What is the simplified value of 39/26?
39/26 divides top and bottom by 13 to give 3/2.
If |n-2| = 10, what is the sum of the two possible values of n?
|n – 2| = 10 gives n – 2 = 10 or n – 2 = -10, so n = 12 or n = -8. Their sum is 4.
The capacity of a cuboidal tank is 50000 liters of water. Find the breadth of the tank, if its length and depth are respectively 2.5 m and 10 m.
50,000 litres = 50 cubic metres. Volume = length x breadth x depth, so 50 = 2.5 x b x 10 = 25b, giving b = 2 m.
At simple interest, a sum becomes 3 times in 20 years. In how many years will it double at the same rate of interest?
If the sum triples, the interest earned equals twice the principal over 20 years, so the rate is 200/20 = 10% per year. To double, the interest must equal the principal, needing 100/10 = 10 years.
The discount price of a book is 20% less than the retail price. James manages to purchase the book at 30% off the discount price at a special book sale. What percent of the retail price did James pay?
The discount price is 0.8 of retail, and James pays 0.7 of that: 0.8 x 0.7 = 0.56. So he pays 56% of the retail price.
A car moves at a speed of 55 km/h. How much distance will it cover in 12 minutes?
12 minutes is 12/60 = 0.2 hours. Distance = 55 x 0.2 = 11 km.
If point A is (4, -1) and point B is (3, 5), what is the square of the distance AB between them?
The square of the distance = (4 – 3)^2 + (-1 – 5)^2 = 1 + 36 = 37.
If Akbar had $12 and spent $8.4, how much money is left?
12 – 8.4 = 3.6 dollars.
A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at simple rate of interest. What is the rate of interest?
SI = 15,500 – 12,500 = 3,000. Rate = SI x 100 / (P x T) = 3,000 x 100 / (12,500 x 4) = 6%.
About the PPSC Mathematics Past Paper 2025
Every MCQ above is taken from the Punjab Public Service Commission (PPSC) Mathematics papers held in 2025, 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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