PPSC Mathematics Past Paper 2019 Solved MCQs with Answers
Solved Mathematics MCQs from the PPSC 2019 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 2019 paper and verified before publication.
In mathematics, a solution to an equation that emerges from the process of solving the problem but is not a valid solution to the problem is called an _______ solution?
A solution that appears while solving but does not satisfy the original equation is called an extraneous solution. It typically arises after squaring both sides or clearing denominators.
When a triangle has two congruent sides, it is called an _______ triangle?
A triangle with two congruent sides is isosceles.
The ______ is equal to the sum of all the values in the data divided by the number of values in the data?
The mean is the sum of all values divided by the number of values.
A ______ is a representation of a frequency distribution by means of rectangles whose widths represent class intervals and whose areas are proportional to the corresponding frequencies?
A histogram represents a frequency distribution using rectangles whose widths are the class intervals and whose areas are proportional to the frequencies.
A horse runs around a ground twice and covers a distance of 8 km, one side of square ground is?
Two laps cover 8 km, so one lap, the perimeter, is 4 km. A square has four equal sides, so each side is 1 km.
Ratio of A:B:C is 5:2:4. If C gets 2000 more than B, how much does B get?
In the ratio 5 : 2 : 4, C exceeds B by 2 parts. Since that difference is 2,000, one part is 1,000 and B receives 2 x 1,000 = 2,000.
In a 60-liter mixture, the ratio of milk and water is 2:1. How much water must be further added to make the ratio 1:2?
In 60 litres at 2:1 there are 40 litres of milk and 20 of water. For a 1:2 ratio with milk fixed at 40, the water must become 80, so 60 litres must be added.
Complete the series: 1, 1, 8, 4, 27, 9, __?
The series interleaves cubes and squares: 1, 8, 27 with 1, 4, 9. The next cube is 4^3 = 64.
If Jack needs 2.5 pints of cream to make a dessert. How many pints will he need to make 3 desserts?
2.5 x 3 = 7.5 pints.
Ali can type at a speed of 25 words per minute. How many words can he type in one hour?
25 words per minute x 60 minutes = 1,500 words.
If the arithmetic mean of 8, 12, 15, 21, x and 11 is 17 then what is x?
The six values must total 6 x 17 = 102. The five known values sum to 67, so x = 35.
Which number will complete the series: 8, 13, 10, 15, 12, 17, 14, ?
The series alternates +5 and -3: 8, 13, 10, 15, 12, 17, 14. Next comes 14 + 5 = 19.
If Mary traveled 116 miles on day 1, 130 miles on day 2, 114 miles on day 3. How many miles per day did she average?
Total = 116 + 130 + 114 = 360 miles over 3 days, an average of 120 miles per day.
Find the average of 8, 13, 25, 43 and 11?
Sum = 8 + 13 + 25 + 43 + 11 = 100 over 5 values, giving 20.
Ahmad reads 24 pages of a book in 15 minutes. The rate of pages read per minute by him will be?
24 pages / 15 minutes = 1.6 pages per minute.
The length and breadth of a rectangle are in the ratio 3:1. If the breadth is 7 cm, then the length of the rectangle is?
With ratio 3 : 1 and breadth 7, the length is 3 x 7 = 21 cm.
Solve: 6.334 x 10000?
6.334 x 10,000 moves the point four places: 63,340.
The number of elements in the power set of {1,2,3} is?
A set with n elements has 2^n subsets, so {1,2,3} has 2^3 = 8.
A patient requires a 30% decrease in the dosage of his medication. His current dosage is 340 mg. What will his dosage be after the decrease?
A 30% decrease leaves 70%: 340 x 0.7 = 238 mg.
If x=3, then x^3 is?
3^3 = 27.
The ratio 35:84 in simplest form is?
Dividing 35 : 84 by 7 gives 5 : 12.
Solve sqrt(1.44)?
1.2 x 1.2 = 1.44, so the square root of 1.44 is 1.2.
The medians of a triangle cut each other in the ratio?
The medians of a triangle meet at the centroid, which divides each median in the ratio 2 : 1 from the vertex.
9 is 1/3% of what number?
One third of one per cent is 1/300. So n/300 = 9, giving n = 2,700.
A solution of water and sugar contains 10% sugar. The solution's weight is 8 kg. When 2 kg of water is added to this solution, the percentage of sugar becomes?
8 kg at 10% contains 0.8 kg of sugar. Adding 2 kg of water makes 10 kg, so the sugar is 0.8/10 = 8%.
A is twice as good a workman as B and together they finish a piece of work in 18 days. In how many days will B alone finish the work?
A works twice as fast as B, so if B does 1 unit a day A does 2, and together 3 units take 18 days. B alone needs 3 x 18 = 54 days.
If you pay $22.90 for a DVD that includes a 7% sales tax, what is the price of the DVD before the sales tax?
The price includes 7% tax, so pre-tax = 22.90 / 1.07 = 21.40 dollars.
The value of 1/3 of 24 is?
One third of 24 is 8.
Length and width of a field are in the ratio 5:3. If the width of the field is 42 m then its length is?
With ratio 5 : 3 and width 42, one part is 14, so the length is 5 x 14 = 70 m.
Aslia has three types of balls: red, green and blue. If their ratio is 2:3:5, what percentage of balls are green?
The parts total 2 + 3 + 5 = 10, so green is 3/10 = 30%.
Income of A is 25% less than B. How much percent would B’s income be more than that of A?
If B earns 100 then A earns 75. B exceeds A by 25 out of 75, that is 25/75 = 33 and 1/3 per cent.
Complete the series: x, 9, 25, 49, 81, 121. Find the value of x.
The terms are the squares of odd numbers: 1, 9, 25, 49, 81, 121. So x = 1^2 = 1.
Total number of students in a class is 95. If the total number of girls in the class is 45, then the ratio of the total number of boys to the total number of girls is?
Boys = 95 – 45 = 50. The ratio of boys to girls is 50 : 45 = 10 : 9.
Sam bought a 12 pack of soda for $5.40. How much did he pay per can of soda?
5.40 / 12 = 0.45 dollars per can.
Which expression correctly calculates what percentage 12 is of 36?
To find what percentage 12 is of 36, divide the part by the whole and multiply by 100: (12/36) x 100.
Decimal form of 5.3% is?
5.3% = 5.3/100 = 0.053.
What is the largest perfect square between 4 and 50?
The perfect squares between 4 and 50 are 9, 16, 25, 36 and 49. The largest is 49.
Solve 8 ÷ 0.2?
8 / 0.2 = 80/2 = 40.
3 boxes have some average weight. When one box which weighs 89 kg is replaced by another box, the average weight increases by 5 kg. How much does the new box weigh?
Three boxes with the average rising by 5 kg means the total rose by 15 kg. The new box weighs 89 + 15 = 104 kg.
By converting 142.5% into decimal, the answer will be?
142.5% = 142.5/100 = 1.425.
A ratio equivalent to 3: 7 is?
Multiplying both parts of 3 : 7 by 3 gives 9 : 21.
The average of 5 quantities is 6. The average of 3 of them is 4. What is the average of the remaining 2 numbers?
Five quantities average 6, a total of 30. Three of them average 4, a total of 12. The remaining two total 18, averaging 9.
The ratio of cost price and selling price is 4: 5. What is the profit percent?
If cost is 4 and selling price 5, the profit is 1 on a cost of 4, that is 25%.
How many subsets does an empty set have?
The empty set has exactly one subset, the empty set itself.
A TV is purchased at Rs. 5000 and sold at Rs. 4000, find the loss percent?
Loss = 5,000 – 4,000 = 1,000. Percentage = 1,000/5,000 x 100 = 20%.
A man can do a piece of work in 5 days, but with the help of his son he can do it in 3 days. In what time can the son do it alone?
The man does 1/5 per day and together they do 1/3. So the son does 1/3 – 1/5 = 2/15 per day, taking 15/2 = 7.5 days.
A Batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after the 17th inning?
Let the average after 17 innings be x. The first 16 averaged x – 3, so 16(x-3) + 87 = 17x. That gives 16x – 48 + 87 = 17x, so x = 39.
What is the square root of 0.16?
0.4 x 0.4 = 0.16, so the square root of 0.16 is 0.4.
The cube root of 0.000216 is?
0.06 x 0.06 x 0.06 = 0.000216, so the cube root is 0.06.
Solve: 840 ÷ 14 + 40?
Division first: 840/14 = 60. Then 60 + 40 = 100.
A square region has an area of 2304 m². Find its perimeter?
The side is sqrt(2304) = 48 m, so the perimeter is 4 x 48 = 192 m.
The arithmetic mean between 4 and 6 is?
The arithmetic mean of 4 and 6 is (4+6)/2 = 5.
If x% of 60 = 48 then x is?
x% of 60 = 48 gives x = 48 x 100 / 60 = 80.
If the average of 5, 6, 7 and X is 10. What is the value of 'X'?
The four values must total 4 x 10 = 40. Since 5 + 6 + 7 = 18, X = 22.
A train running with a speed of 60 km/h crosses a pole in 9 seconds. What is the length of the train?
60 km/h = 16.67 m/s. Crossing a pole in 9 seconds means the train's own length = 16.67 x 9 = 150 m.
A number is as much greater than 36 as it is less than 86. Find the number?
n – 36 = 86 – n gives 2n = 122, so n = 61.
What number increased by 20% of itself is equal to 102?
The number plus 20% of itself is 1.2n = 102, so n = 85.
To convert a decimal number into a binary number, we use the method of repeated?
Decimal to binary conversion uses repeated division by 2, recording the remainders.
Find the average of all numbers between 6 and 34 which are divisible by 5?
The multiples of 5 between 6 and 34 are 10, 15, 20, 25 and 30. Their average is the middle value, 20.
Solve: 30% of 3300?
30% of 3,300 = 0.30 x 3,300 = 990.
Evaluate: √(248) + √64?
sqrt(248) = sqrt(4 x 62) = 2 sqrt(62), and sqrt(64) = 8. So the total is 8 + 2 sqrt(62).
Given that 543 x 21 = 11403. Find the value of: 1140.3 ÷ 5.43?
1140.3 / 5.43 has the same digits as 114030 / 543. Since 543 x 21 = 11,403, we get 543 x 210 = 114,030, so the answer is 210.
The average of ten positive numbers is x. If each number is increased by 10%, what is the new average?
Increasing every number by 10% increases the total by 10%, and therefore the average too. The new average is 1.1x.
A speed of 14 meters per second is the same as?
To convert m/s to km/h multiply by 3.6: 14 x 3.6 = 50.4 km/h.
Reeya obtained 65, 67, 78, 82 and 85 out of 100 in different subjects, what will be the average?
Sum = 65 + 67 + 78 + 82 + 85 = 377 over 5 subjects, giving 75.4.
By converting 75% into fraction, answer will be?
75% = 75/100 = 3/4.
Alia can complete an assignment in 5 days and Babar can complete the same assignment in 20 days. The time taken by both Alia and Babar to complete the assignment working together is?
Alia does 1/5 per day and Babar 1/20. Together 1/5 + 1/20 = 1/4, so 4 days.
Asghar can do a job in 60 days. And both Asghar and Babar can do the same job in 20 days working together. Babar alone can do same job in?
Together they do 1/20 per day and Asghar alone does 1/60. So Babar does 1/20 – 1/60 = 1/30, that is 30 days.
If a:b=2:3 and b:c=4: 3, then find a:b:c?
a : b = 2 : 3 = 8 : 12, and b : c = 4 : 3 = 12 : 9. With b common, a : b : c = 8 : 12 : 9.
A doll is sold for Rs. 220. What was the cost of doll if rate of profit was 10% of the cost?
A 10% profit means the selling price is 1.1 times cost, so cost = 220 / 1.1 = 200.
If Kayla left a $10.47 tip on a breakfast that cost $87.25, what percentage was the tip?
10.47 / 87.25 x 100 = 12%.
Find out the average of A and B if the given value of 16 A + 16 B = 48?
16A + 16B = 48 gives A + B = 3, so the average is 3/2 = 1.5.
For the series, what is the next term: 4, 6, 9, 13, __?
The differences grow by one each time: +2, +3, +4, so the next is +5, giving 13 + 5 = 18.
Muzammil buys an old scooter for Rs. 4700 and spends Rs. 500 on its repairs. If he sells the scooter for Rs. 5800, his gain percent is?
Total cost = 4,700 + 500 = 5,200. Gain = 5,800 – 5,200 = 600. Percentage = 600/5,200 x 100 = 11.54%.
If 1 day work = 1/20 then time required to finish the job (in days)?
If one day's work is 1/20 of the job, the whole job takes 20 days.
Oscar purchased a new hat that was on sale for $5.06. The original price was $9.20. What percentage discount was the sale price?
The reduction is 9.20 – 5.06 = 4.14. As a percentage of the original, 4.14/9.20 x 100 = 45%.
For the series, what is the next term: 36, 34, 30, 28, 24, __?
The differences alternate -2 and -4: 36, 34, 30, 28, 24. The next step is -2, giving 22.
Two numbers are in the ratio 7: 9, if the sum of the numbers is 112, then the larger number is?
The parts total 7 + 9 = 16, so one part is 112/16 = 7. The larger number is 9 x 7 = 63.
Solve 12 / 20?
12 / 20 = 0.6.
Solve 5 / 0.5?
5 / 0.5 = 10.
Three numbers are in the ratio 4:5:6 and their average is 30. The largest number is?
The parts total 15 and the average is 30, so the sum is 90 and one part is 6. The largest is 6 x 6 = 36.
The average of four consecutive odd numbers is 24. Find the largest number?
Four consecutive odd numbers averaging 24 are 21, 23, 25 and 27. The largest is 27.
What is 2^8?
2^8 = 256.
Evaluate: √6084?
78 x 78 = 6,084, so the square root is 78.
A school has a strength of 550 in the year 2017 with an increase of 12% in 2018. What is the total strength of school?
550 x 1.12 = 616.
12.5% is Equal to which fraction?
12.5% = 12.5/100 = 1/8.
The ratio of 3.5 kg to 280 gm is?
3.5 kg = 3,500 g. The ratio 3,500 : 280 divides by 140 to give 25 : 2.
A table listed at Rs. 160 is marked 20% off. What is the sale price?
A 20% reduction leaves 80%: 160 x 0.8 = 128.
A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?
Passing the post takes 8 seconds for the train's own length L, and the bridge takes 20 seconds for L + 264. Equal speeds give L/8 = (L+264)/20, so 20L = 8L + 2112 and L = 176 m. Speed = 176/8 = 22 m/s = 79.2 km/h.
How many tiles of dimension 10 square inch are required to cover a floor of dimension of 5 feet by 4 feet?
The floor is 60 x 48 = 2,880 square inches. Each tile covers 10 square inches, so 2,880/10 = 288 tiles.
After spending 4/9 of her money, a girl has 25 rupees left. How much did she spend?
Having spent 4/9, she is left with 5/9, which is 25 rupees. So the whole is 45 and she spent 45 – 25 = 20.
One kilometer is equal to?
One kilometre equals 1,000 metres.
About the PPSC Mathematics Past Paper 2019
Every MCQ above is taken from the Punjab Public Service Commission (PPSC) Mathematics papers held in 2019, 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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