PPSC Mathematics Past Paper 2023 Solved MCQs with Answers
Solved Mathematics MCQs from the PPSC 2023 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 2023 paper and verified before publication.
Which of the following fractions is greater than 3/4 and less than 5/6?
3/4 = 0.75 and 5/6 = 0.833. Since 19/24 = 0.7917, it lies between the two.
A car travels at the speed of 36 km per hour. What is the distance traveled by the car within 20 second in meter?
36 km/h = 36000/3600 = 10 m/s. In 20 seconds the car covers 10 x 20 = 200 metres.
Find the height of a parallelogram whose area is 54 cm² and the base is 15 cm?
Height = area / base = 54 / 15 = 3.6 cm.
If 3x-8=-23, what is the value of 6x – 7?
3x – 8 = -23 gives 3x = -15, so x = -5. Then 6x – 7 = -30 – 7 = -37.
A manufacturer of TV sets produced 600 units in the third year and 700 units in the seventh year. Assuming that the production increases uniformly by a fixed number every year, find the production in the first year?
a3 = 600 and a7 = 700, so 4d = 100 and d = 25. Then a1 = 600 – 2(25) = 550 sets.
The ratio of ages of two students is 3:2. One is older to the other by 5 years. What is the age of younger student?
The ages are 3k and 2k, differing by k = 5. So the younger is 2 x 5 = 10 years.
The radius of a circle is 10 cm and the length of one of its chords is 12 cm then the distance of chord from the centre is?
Half the chord is 6 cm. The distance from the centre = sqrt(10^2 – 6^2) = sqrt(64) = 8 cm.
What is 20% as a fraction?
20% = 20/100 = 1/5.
If 1/4 writing, 1/6 reading and 1/8 designing are participated in different contest and 33 participants of mathematics, then total number of participants are?
The three contests take 1/4 + 1/6 + 1/8 = 13/24 of the participants, leaving 11/24 for mathematics. So 11/24 of the total is 33, giving a total of 72.
A vehicle has 22 units of fuel left after the 4th lap and 18 units after the 7th lap. If fuel is used at a constant rate, after how many laps will the fuel run out?
Fuel falls from 22 to 18 over 3 laps, a rate of 4/3 per lap. Starting from 22 at lap 4, it reaches zero after a further 22 / (4/3) = 16.5 laps, that is at lap 20.5.
What is the sum of the first 5 composite numbers?
The first five composite numbers are 4, 6, 8, 9 and 10. Their sum is 37.
The decimal equivalent of the binary number 10100 is?
10100 in binary = 16 + 4 = 20 in decimal.
A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60 degrees with the wall, what is the height of the wall?
The angle is measured with the wall, so the wall is the adjacent side: height = 15 x cos(60) = 15 x 0.5 = 7.5 m.
If Gohar salary 25% less than Babar salary, then how much percent Babar salary greater than Gohar?
If Babar earns 100 then Gohar earns 75. Babar exceeds Gohar by 25 out of 75, that is 25/75 = 33.33%.
The average height of five pupils is 68 inches. If one is 70 inches and three others are 76 inches, then what is the height (in inches) of the fifth pupil?
Five pupils average 68, a total of 340. The four known heights are 70 + 76 + 76 + 76 = 298, so the fifth is 340 – 298 = 42 inches.
The value of an article which was purchased 2 years ago, depreciates at 12 % per annum. If its present value is Rs. 9680, the price at which it was purchased is?
Depreciation gives 9680 = P x (0.88)^2 = 0.7744P, so P = 9680 / 0.7744 = 12,500 exactly. The closest option offered is 12,500.65.
If 30 men working 9 h per day can reap a field in 16 days, in how many days will 36 men reap the field working 8 h per day?
The work is 30 x 9 x 16 = 4,320 man-hours. With 36 men at 8 hours a day, days = 4320 / (36 x 8) = 15.
The angles of a triangle are (x-35), (x- 25) and (1/2x-10), find x?
The angles sum to 180: (x-35) + (x-25) + (x/2 – 10) = 180. That gives 2.5x – 70 = 180, so 2.5x = 250 and x = 100.
The principal which will amount to Rs. 270.40 in 2 years at the rate of 4% per annum compound interest is?
270.40 = P x (1.04)^2 = 1.0816P, so P = 270.40 / 1.0816 = 250 rupees.
A car travels 100 km at a speed of 60 km/h and returns with a speed of 40 km/h. Calculate the average speed for the whole journey?
For equal distances the average speed is the harmonic mean: 2 x 60 x 40 / (60 + 40) = 4800/100 = 48 km/h. Note it is not 50.
Average weight of 10 people increased by 1.5 kg when one person of 45 kg is replaced by a new man. Then weight of the new man is?
The average of 10 people rose by 1.5 kg, so the total rose by 15 kg. The new man weighs 45 + 15 = 60 kg.
The sum of the first five prime numbers is?
The first five primes are 2, 3, 5, 7 and 11. Their sum is 28.
If principal = Rs. 1,00,000, Rate of interest =10% compounded half yearly. Find amount after one year?
Compounded half-yearly means 5% twice: 100,000 x (1.05)^2 = 110,250.
A man walked for 1/3 hour and then got an automobile ride for 1/2 hour. What part of total time consumed did he ride on automobile?
Total time = 1/3 + 1/2 = 5/6 hour. The ride is (1/2) / (5/6) = 3/5 of the total.
How many cubes of 1 cm edge can be cut from a cuboid of the dimension of 10 cm x 12 cm x 15 cm?
Volume = 10 x 12 x 15 = 1,800 cubic cm, and each small cube is 1 cubic cm, so 1,800 cubes.
If the price of a carpet 8-meter-long and 3-meter-wide is Rs. 6288, what will be the price of a 12-meter-long and 6-meter-wide carpet?
The first carpet is 24 sq m for 6,288, so the rate is 262 per sq m. The second is 12 x 6 = 72 sq m, costing 72 x 262 = 18,864.
If x*y = x^2 + y^2 – xy, then the value of 9*11 is?
9*11 = 9^2 + 11^2 – (9)(11) = 81 + 121 – 99 = 103.
If 144/0.144 = 14.4/x then what will be the value of x?
144 / 0.144 = 1000. So 14.4 / x = 1000, giving x = 14.4/1000 = 0.0144.
If a+b=-2 then (a+b)^3 is?
(a+b)^3 = (-2)^3 = -8.
Kriya deposits an amount of Rs. 65800 to get a simple interest at the rate of 14% per annum for 4 years. What total amount will Kriya get at the end of 4 years?
SI = 65,800 x 14 x 4 / 100 = 36,848. Total = 65,800 + 36,848 = 102,648.
A photograph measuring 5 cm by 7 cm is enlarged in the ratio of 7:5. What are the new dimensions (length, width) of the picture?
Enlarging in the ratio 7:5 multiplies each side by 7/5. So 7 x 7/5 = 9.8 cm and 5 x 7/5 = 7 cm.
A Motor Cycle was bought for Rs. 60000 and sold for Rs. 66000. His percentage profit is?
Profit = 66,000 – 60,000 = 6,000. Percentage = 6,000/60,000 x 100 = 10%.
Hamza has Rs. 2000. He bought stationery which is 14% of 2000. How much rupee is he left with?
14% of 2,000 = 280. He is left with 2,000 – 280 = 1,720.
3.275 is equal to?
0.275 = 275/1000 = 11/40, so 3.275 = 3 and 11/40.
There are 120 girls and 50 boys. Find the ratio of boys to girls?
Boys to girls = 50 : 120, which divides by 10 to give 5 : 12.
Solve the cube root of 64, divided by 3?
The cube root of 64 is 4, and 4 divided by 3 is 4/3.
What is the LCM of the 6th and 7th term in the sequence an=3n+2?
With an = 3n + 2, the 6th term is 20 and the 7th is 23. Since 23 is prime, the LCM is 20 x 23 = 460.
If the purchase amount is Rs.20000 and sell price is Rs.16000 then the loss is how much percent?
Loss = 20,000 – 16,000 = 4,000. Percentage = 4,000/20,000 x 100 = 20%.
Ali took a loan of Rs.50,000 at 9% rate of interest for 2 years at simple interest to renovate his house. How much extra amount does he pay in 2 years?
The extra amount is the interest: 50,000 x 9 x 2 / 100 = 9,000.
A merchant has announced 25% rebate on prices of ready-made garments at the time of sale. If a purchaser needs to have a rebate of Rs. 400, then how many shirts, each costing Rs. 320, should he purchase?
Each shirt gives a rebate of 25% of 320 = 80. To obtain 400 he needs 400/80 = 5 shirts.
The highest power (degree) of a linear equation is?
A linear equation has highest power, or degree, 1.
If 10 men can construct a building in 40 days. How long will it take 1 man to do this work?
The job is 10 x 40 = 400 man-days, so one man alone needs 400 days.
The true discount on Rs. 1760 due after a certain time at 12% per annum is Rs. 160. The time after which it is due is?
Present worth = 1760 – 160 = 1600. Since TD = PW x R x T / 100, 160 = 1600 x 12 x T / 100 = 192T, so T = 5/6 of a year.
Solve -8/20 -(+9/2)-1/2?
-8/20 = -0.4. Then -0.4 – 4.5 – 0.5 = -5.4.
An open rectangular tank that is 4m long, 2m wide and 4.8m high, is initially three-quarters filled with water. Find the depth of water in the tank after 4000 liters of water are added to it?
The tank holds 4 x 2 x 4.8 = 38.4 cubic m. Three quarters full means a depth of 3.6 m, that is 28.8 cubic m. Adding 4,000 litres, or 4 cubic m, gives 32.8 cubic m, so the depth is 32.8 / 8 = 4.1 m.
The sum of two numbers, one of which is two thirds of the other, is 45. Find the smaller number?
If the larger is x then x + (2/3)x = 45, so (5/3)x = 45 and x = 27. The smaller is 45 – 27 = 18.
How many numbers of two digits are divisible by 9?
Two-digit multiples of 9 run from 18 to 99, that is 18, 27, …, 99, which is 10 numbers.
6×6 inch tiles cost Rs.60 each. For a room area of 10×6 feet, what is the total cost of tile flooring?
The room is 10 x 6 = 60 sq ft. Each tile is 6 x 6 inches = 0.5 x 0.5 = 0.25 sq ft, so 240 tiles are needed. Cost = 240 x 60 = 14,400.
If 35 labors dig 805 cubic meters of earth in 5 hours, how much earth will 30 labors dig in 6 hours?
Rate per labourer-hour = 805 / (35 x 5) = 4.6 cubic m. Then 30 labourers for 6 hours dig 30 x 6 x 4.6 = 828 cubic m.
A positive number when decreased by 4 becomes 21 times its reciprocal. The number is?
n – 4 = 21/n gives n^2 – 4n – 21 = 0, that is (n-7)(n+3) = 0. The positive value is 7.
12 men can do a piece of work in 10 days. How many men would be required to do the same work in 8 days?
The job is 12 x 10 = 120 man-days. To finish in 8 days needs 120/8 = 15 men.
Find the value of x when y=5, if x varies directly as (4y-1) and x=14 when y=2?
x = k(4y – 1). With x = 14 at y = 2, 14 = k(7) so k = 2. At y = 5, x = 2(19) = 38.
The total cost of 12 pens and 5 pencils is equal to Rs.111. Also, the cost of 1 pencil is Rs.5 less than the cost of 1 pen. What will be the cost of 8 pens and 9 pencils?
12p + 5q = 111 with q = p – 5. So 12p + 5p – 25 = 111, giving 17p = 136 and p = 8, q = 3. Then 8p + 9q = 64 + 27 = 91.
Julie has a square fence that enclosed her garden. She decided to expand her garden by making each side of the fence 10 percent longer. After this expansion, the area of Julie's garden will have increased by what percent?
Each side grows by 10%, so the area grows by (1.1)^2 = 1.21, an increase of 21%.
Increase 224 in the ratio 7:9. The new number is?
Increasing in the ratio 7:9 multiplies by 9/7: 224 x 9/7 = 288.
Ahmad is as much younger than Saeed as he is older than Tanveer. If the sum of the ages of Saeed and Tanveer is 48 years. What is the age of Ahmad?
Ahmad is as much younger than Saeed as he is older than Tanveer, so Ahmad is the midpoint: 2 x Ahmad = Saeed + Tanveer = 48, giving Ahmad = 24.
10% of the number 391680 is?
10% of 391,680 = 39,168.
A can do a work in 6 days and B can do the same work in 12 days. How long will it take if A and B work together?
A does 1/6 per day and B does 1/12 per day. Together 1/6 + 1/12 = 1/4, so 4 days.
A steam shovel excavates 2 cubic yards every 40 seconds. At this rate, the amount excavated in 45 minutes is?
45 minutes = 2,700 seconds, which is 2700/40 = 67.5 intervals. Each moves 2 cubic yards, so 67.5 x 2 = 135 cubic yards.
A 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 will B alone take to do it?
A alone is 1/4 per hour. A and C give 1/2, so C = 1/2 – 1/4 = 1/4. B and C give 1/3, so B = 1/3 – 1/4 = 1/12, that is 12 hours.
The length and breadth of a rectangular drawing room of a house are 18 ft and 13 ft respectively. If the height of the room is 10 ft and the cost of painting is Rs.40 per square ft, find the cost of painting the drawing room walls.
Wall area = perimeter x height = 2(18 + 13) x 10 = 620 sq ft. Cost = 620 x 40 = 24,800.
The value of x satisfying the equation 7x+1=4x-8 is?
7x + 1 = 4x – 8 gives 3x = -9, so x = -3.
A 5m long ladder is placed against a wall with its foot 2 m from the wall. How high up the wall does the ladder reach?
By Pythagoras the height = sqrt(5^2 – 2^2) = sqrt(21) m.
The diameter of a wheel of a car is 48 cm. If the car travels at an average speed of 3.5 km/h. The number of revolutions made by the wheel per minute is?
Circumference = pi x 48 = 150.8 cm. Speed 3.5 km/h = 350,000 cm/h = 5,833.3 cm/min. Revolutions per minute = 5833.3 / 150.8 = 38.68.
Express 0.286 as a percentage?
0.286 x 100 = 28.6%.
The difference between three times a number and four more than two times the number can be represented by the expression, where x is the number?
Three times the number is 3x, and four more than twice the number is 2x + 4. The difference is 3x – (2x + 4) = x – 4.
In Excel, Columns are labelled as?
In Excel the columns are labelled with letters A, B, C and so on, while rows are numbered.
If 2.5% of a certain number is 250,000, what is the actual value of that number?
2.5% of n = 250,000, so n = 250,000 / 0.025 = 10,000,000.
The price of a share in the stock exchange dropped from Rs. 62.50 to Rs. 52.50 in a week. What was the percentage change in the price of the share?
The drop is 62.50 – 52.50 = 10. Percentage change = 10 / 62.50 x 100 = 16%.
If 40% of a number is equal to two-third of another number, what is the ratio of the first number to the second number?
0.4a = (2/3)b, so a/b = (2/3)/0.4 = 5/3, that is 5 : 3.
The arithmetic mean is 25 and the sum of observations is 350, then the number of observations is?
Number of observations = sum / mean = 350 / 25 = 14.
Ghafoor went to the stationers and bought things worth Rs. 25. Out of this, 30 paise went as sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax-free items?
The tax of 30 paise at 6% means taxable goods cost 0.30/0.06 = 5 rupees. The tax-free items then cost 25 – 5 – 0.30 = 19.70, which rounds to the option of 20.
If Ahmed purchases a Watch for Rs 600 and pays 15% sales tax, the total amount spent on purchase is?
600 x 1.15 = 690 rupees.
Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?
Total votes = 1,136 + 7,636 + 11,628 = 20,400. The winner's share = 11,628 / 20,400 x 100 = 57%.
If the price of petrol is increased by 20%, by what percentage should the consumption be decreased by the consumer if the expenditure on petrol remains unchanged?
To keep spending unchanged after a 20% rise, consumption must fall by 20/120 = 16.67%.
The number of observations is 30 and the value of arithmetic mean is 15, then sum of all values is?
Sum = mean x number = 15 x 30 = 450.
If a:b=2:3 and b:c=4:3, then find a:b:c.
Make b common: a : b = 2 : 3 = 8 : 12, and b : c = 4 : 3 = 12 : 9. So a : b : c = 8 : 12 : 9.
There are two numbers and their ratio is 3:9. If we subtract 9 from both numbers then their ratio becomes 12:13, what is value of the larger number?
Let the numbers be 3k and 9k. Then (3k-9)/(9k-9) = 12/13, giving 39k – 117 = 108k – 108, so 69k = -9 and k = -3/23. The larger number is 9k = -27/23.
Salaries of Ravi and Sumit are in the ratio 2:3. If the salary of each is increased by Rs 4000, the new ratio becomes 40:57. What is Sumit present salary?
Salaries are 2k and 3k. Then (2k+4000)/(3k+4000) = 40/57, giving 114k + 228,000 = 120k + 160,000, so 6k = 68,000. Sumit gets 3k = 34,000.
A car is travelling at a speed of 90 km/hr. In how many minutes it will cover 450 km?
Time = 450 / 90 = 5 hours = 300 minutes.
If a bag of 40 kg rice costs Rs. 3200, how much rice can be bought in Rs. 4800?
40 kg costs 3,200, so the rate is 80 per kg. For 4,800 he gets 4800/80 = 60 kg.
Akbar wants to distribute some amount among his four partners (A, B, C, D) respectively in proportion 1:2:3:4, can you guess the share of B if total amount is Rs. 80,000?
The parts total 1 + 2 + 3 + 4 = 10. B's share = 2/10 x 80,000 = 16,000.
A university allocates 360 seats for three disciplines (Electrical, Mechanical and Civil) in the ratio 2:3:4. How many seats are there in Mechanical?
The parts total 2 + 3 + 4 = 9, so one part is 360/9 = 40 seats. Mechanical takes 3 parts = 120.
Mr. A and B invest in ratio 1:2. Each receives Rs. 5000 profit, and their new amounts are in ratio 18:24. What is B’s amount after profit?
Investments are k and 2k. After 5,000 profit each, (k+5000)/(2k+5000) = 18/24 = 3/4, giving 4k + 20,000 = 6k + 15,000, so k = 2,500. B's amount = 5,000 + 5,000 = 10,000.
Ali obtained an average marks of 48 in Physics, Chemistry and Biology. What are total marks of three subjects?
Total = average x number of subjects = 48 x 3 = 144.
Shahzad family has an average age of 72 years. If the family has total 4 members, what is their collective age?
Collective age = 72 x 4 = 288 years.
The average of three numbers is 54. If two numbers are 48 and 58, what is the third number?
The three total 54 x 3 = 162. The third number = 162 – 48 – 58 = 56.
On calculation, the mean (average) of 15 numbers was 64. One of the numbers 24 was misread as 34. What is the correct mean?
The recorded total was 15 x 64 = 960. Correcting 34 to 24 lowers it by 10 to 950, so the true mean is 950/15 = 63 and 1/3.
On a Tuesday morning, 60 workers could not present themselves for work. If there are 540 workers in the factory, what percent of the workers were present?
Present = 540 – 60 = 480. Percentage present = 480/540 x 100 = 88.8%.
A workman bought a bike for Rs. 75,500 at a 20% discount. How much did he save?
The saving is the 20% discount on 75,500, that is 0.20 x 75,500 = 15,100.
When we write all the numbers from 1 to 100, how many times do we write the digit 7?
The digit 7 appears 10 times in the units place (7, 17, …, 97) and 10 times in the tens place (70 to 79), giving 20 in total.
Write the next number of the given series: 1/3, 2/9, 1/27, 2/81, …?
The numerators alternate 1, 2, 1, 2 and the denominators are powers of 3: 3, 9, 27, 81. The next term is 1/243.
Given the series: ABD, BCE, CDF, DEG, what should follow?
Each letter advances by one: ABD, BCE, CDF, DEG, so the next is EFH.
Four persons can cross a bridge in 3, 7, 13, 17 minutes. Only two can cross at a time. Find the minimum time taken by the four to cross the bridge?
Send 3 and 7 across (7 min), 3 returns (3), send 13 and 17 (17), 7 returns (7), then 3 and 7 cross (7). Total = 7 + 3 + 17 + 7 + 7 = 41 minutes.
Two trains each of length 150m are running in opposite directions with the same speed. If they cross each other in 15 seconds, what is the speed of each train in km per hour?
Together they cover 150 + 150 = 300 m in 15 s, a relative speed of 20 m/s. Moving in opposite directions the relative speed is twice one train's speed, so each travels at 10 m/s = 36 km/h.
About the PPSC Mathematics Past Paper 2023
Every MCQ above is taken from the Punjab Public Service Commission (PPSC) Mathematics papers held in 2023, 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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