PPSC Mathematics Past Paper 2016 Solved MCQs with Answers
Solved Mathematics MCQs from the PPSC 2016 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 2016 paper and verified before publication.
The average (arithmetic mean) of 5, 10, 15, and z is 20. What is z?
The four values must total 4 x 20 = 80. Since 5 + 10 + 15 = 30, z = 50.
One-fourth of a number exceeds one- sixteenth of the number by 3. Find four times the number?
n/4 – n/16 = 3. Since 4/16 – 1/16 = 3/16, we get 3n/16 = 3, so n = 16 and four times the number is 64.
If thirty years ago my age was 1/6th of what it is now, then what is my present age in years?
n – 30 = n/6 gives 6n – 180 = n, so 5n = 180 and n = 36.
If the ratio of the sides of a triangle is 2 :3:4 and its perimeter is 54 cm, then the measure of the smallest side of the triangle will be?
The parts total 2 + 3 + 4 = 9, so one part is 54/9 = 6. The smallest side is 2 x 6 = 12 cm.
A single letter is selected at random from the word "PROBABILITY", then probability of vowel letter is?
PROBABILITY has 11 letters, of which the vowels are O, A, I and I, that is 4. The probability is 4/11.
Eighty-five percent of the sheep in a herd are male. If 80% of the male and 20% of the female sheep were slaughtered on Eid-ul-Azha, what percent of the entire number of sheep in the herd was left?
Take 100 sheep: 85 male, 15 female. Slaughtered = 80% of 85 + 20% of 15 = 68 + 3 = 71. So 29% were left.
A holiday apartment at Ayubia costs Rs. 25,550 to hire, but a 10% discount is offered for early booking. A deposit of one-fifth of the total bill has to be sent in advance at the time of booking. What deposit would be required when an early booking is made?
After a 10% discount the bill is 25,550 x 0.9 = 22,995. One fifth of that is 4,599.
What is the amount of Zakat a person has to pay if he has Rs. 4,040,000 at a rate of 2.5%?
Zakat = 2.5% of 4,040,000 = 101,000.
If a+3a is 4 less than b + 3b, then a- b?
a + 3a = 4a and b + 3b = 4b. Since 4a is 4 less than 4b, 4a = 4b – 4, so a = b – 1 and a – b = -1.
A person can do a work in 10 days but another can do it in 15 days. In how many days, they will complete the task if work together?
One does 1/10 per day and the other 1/15, together 1/10 + 1/15 = 1/6, so 6 days.
The speed of the train going from Nagpur to Allahabad is 100 km/h while coming back from Allahabad to Nagpur, its speed is 150 km/h. Find the average speed during the whole journey?
For equal distances the average speed is the harmonic mean: 2 x 100 x 150 / (100 + 150) = 30,000/250 = 120 km/h.
The price of one egg is Rs. 5 and in a tray about 30 eggs can be placed. What will be the price of 7 trays of eggs?
One tray of 30 eggs costs 30 x 5 = 150, so 7 trays cost 1,050.
The average of first five multiples of 3 is?
The first five multiples of 3 are 3, 6, 9, 12, 15, evenly spread, so the average is the middle value, 9.
Find the odd one in the series: 835, 734, 642, 751, 853, 981, 532?
In each number the first digit minus the second gives the third: 8-3=5, 7-3=4, 6-4=2, 8-5=3, 9-8=1, 5-3=2. Only 751 fails, since 7-5 is 2, not 1.
A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?
The train covers its own 240 m in 24 seconds, so its speed is 10 m/s. Passing the platform means covering 240 + 650 = 890 m, taking 89 seconds.
Find the odd one out 10 25 45 54 60 75 80?
All the numbers are multiples of 5 except 54.
What does an Acre measure in Marlas?
One acre measures 160 marlas.
How many “Furlongs” make 1 (one) mile?
There are 8 furlongs in one mile.
Sadiq purchased a plot for Rs. 8,000. He sells the plot to Abid at a profit of 20%. Abid in turn sells that plot to Arif at a loss of 10%. The plot costs Arif?
Sadiq sells at 8,000 x 1.2 = 9,600. Abid then sells at a 10% loss: 9,600 x 0.9 = 8,640, which is what the plot costs Arif.
A’s mother is twice as old as A’s brother. A is 6 years younger than his brother but 4 years older than his sister. If A’s sister is 15, his mother’s age is?
The sister is 15, so A is 19 and the brother is 19 + 6 = 25. The mother is twice the brother's age, that is 50.
If 12 years are added to 2/3 age of Rani, she will be three years older than today. What is Rani’s present age?
(2/3)r + 12 = r + 3 gives 9 = r – (2/3)r = r/3, so r = 27.
Six men working 8 hours a day earn Rs 720 per week. 8 men working 6 hours a day will earn per week?
Six men at 8 hours give 48 man-hours for 720. Eight men at 6 hours also give 48 man-hours, so the pay is unchanged at 720.
Mr. Rehraan ordered a car worth Rs. 600,000 and was given a discount. Given that he paid Rs. 570,000 for his new car, calculate the percentage discount he received?
The discount is 600,000 – 570,000 = 30,000, that is 30,000/600,000 x 100 = 5%.
Given opening capital of Rs.16,500, closing capital as Rs.11,350 and drawings were Rs.3,300, then?
Closing capital = opening + profit – drawings, so 11,350 = 16,500 + P – 3,300. That gives P = -1,850, which is a loss of 1,850.
Complete the number series: 1, 2, 3, 6, 9, 18, ___, 54?
The series interleaves two sequences, each tripling: 1, 3, 9, 27 and 2, 6, 18, 54. The missing term belongs to the first, giving 27.
‘A’ is twice as old as ‘B’. Three year ago ‘A’ was three times as old as ‘B’. How old is ‘A’ now?
A = 2B, and three years ago A – 3 = 3(B – 3). So 2B – 3 = 3B – 9, giving B = 6 and A = 12.
At the end of conference the 10 people present all shakes hands with each other once. How many handshakes will there be altogether?
Each handshake involves a pair, so the number is 10C2 = 10 x 9 / 2 = 45.
What function displays row data in a column or column data in a row?
The Transpose function converts row data into a column and column data into a row.
Afzal mixed 40% kerosene solution to 25% kerosene solution hence obtaining 30% kerosene solution mixed. In what ratio were the both solutions mixed?
By alligation the distances from the mean are 40 – 30 = 10 and 30 – 25 = 5. The quantities are in the inverse ratio, so 40% to 25% is 5 : 10 = 1 : 2.
The price of certain items increased by X% per week over two successive weeks. If at the beginning, 2 kg was available for Rs. 80 and after two weeks they were available for Rs. 105.80, what is the value of (1 + X/100)^2?
Two successive rises of X% multiply the price by (1 + X/100)^2. So (1 + X/100)^2 = 105.80/80 = 1.3225.
The Muslim mathematician Al-Khwarizmi is best known for his work in?
Al-Khwarizmi is best known for his work in algebra. The word algebra comes from the title of his book, and the word algorithm from his name.
Complete the series: 2, 4, 16, 256, ?
Each term is the square of the one before: 2, 4, 16, 256. Next is 256^2 = 65,536.
Complete the series: 50, 60, 80, 110, 150, ?
The differences rise by 10 each time: +10, +20, +30, +40. The next step is +50, giving 200.
If 25% of a certain number is 1600, what is 10% of the number?
25% of n = 1,600, so n = 6,400. Then 10% of 6,400 = 640.
Multiply 15,873 x 28?
15,873 x 28 = 444,444.
Divide 3900 ÷ 500?
3,900 / 500 = 7.8.
Calculate the value of x in the equation: 12 – 5x = x + 30?
12 – 5x = x + 30 gives -18 = 6x, so x = -3.
A rectangular floor 18ft x 10ft is to be covered with carpeting that costs Rs. x per sq. yard. In terms of x how many Rupees will the carpeting cost?
The floor is 18 x 10 = 180 square feet. Since 9 square feet make a square yard, that is 20 square yards, costing 20x rupees.
If a machine makes 3 yards of cloth in 2 minutes, how many yards of cloth will the machine make in 50 minutes?
The machine makes 1.5 yards a minute, so in 50 minutes it makes 75 yards.
Simplify: 12 x (13 – 2 x 5)?
Brackets first: 13 – 2 x 5 = 13 – 10 = 3. Then 12 x 3 = 36.
Simplify 4 + 2 x 3 – 6 + 2?
Multiplication first: 2 x 3 = 6. Then 4 + 6 – 6 + 2 = 6.
Complete the number series: 11, 13, 17, 19, 23, 29, 31, 37, 41, _ _?
The terms are consecutive prime numbers, so after 41 comes 43.
In a 100m race, A covers the distance in 36 seconds and B in 45 seconds. In this A beats B by?
A finishes in 36 seconds. In that time B, who needs 45 seconds for 100 m, covers 100 x 36/45 = 80 m. So A beats B by 20 m.
Evaluate 48.95 – 32.006?
48.95 – 32.006 = 16.944.
A woman paid Rs.15000 as down payment on a house if this amount was 20% of the price, what did the house cost?
The down payment of 15,000 is 20% of the price, so the house cost 15,000/0.2 = 75,000.
If 10 men can do a piece of work in 20 days, how long will it take 8 men to do the same job if they work at the same rate?
The job is 10 x 20 = 200 man-days, so 8 men take 200/8 = 25 days.
A toy is sold for RS.220. What was the cost if the rate of profit was 10% of the cost?
A 10% profit means the selling price is 1.1 times the cost, so cost = 220/1.1 = 200.
What is the square root of 6492304?
2,548 x 2,548 = 6,492,304, so the square root is 2,548.
If 70% of students in a school are boys and the number of girls is 504, the number of boys is?
If 70% are boys then 30% are girls, and 30% = 504, so the total is 1,680. Boys = 1,680 – 504 = 1,176.
In a row a student is standing 13th from the right and 8th from the left. How many students are there in total?
The student is counted from both ends, so the total = 13 + 8 – 1 = 20.
The average age of a group of 13 boys is 13. When two more boys join the group, the average rose by 2 years. The sum of the ages of the two new boys is?
13 boys average 13, a total of 169. Fifteen boys averaging 15 total 225. So the two new boys total 225 – 169 = 56.
Find the missing number in the number series: 2, 4, 12, 48, 240, …?
The multipliers rise by one each step: x2, x3, x4, x5. The next is x6, giving 240 x 6 = 1,440.
What comes next in the sequence: 2, 12, 32, 62, 102?
The differences rise by 10: +10, +20, +30, +40. The next step is +50, giving 152.
A box of chocolate bar costs Rs. 32 (inclusive of 10% sales tax), and there are 16 bars in one box. What is the price (excluding 10% sales tax) for one chocolate bar?
The box costs 32 including 10% tax, so the pre-tax price is 32/1.1 = 29.09. Divided among 16 bars that is about 1.8 rupees each.
Complete the series: J, F, M, A, M, ?
The letters are the initials of the months: January, February, March, April, May. The next is June, that is J.
If 50 meters of road makes 10% of the whole length of the road, the length of the road is?
50 metres is 10% of the road, so the whole length is 50/0.10 = 500 metres.
What is the next number in the series: 6, 9, 18, 45, 126, …?
The differences are powers of 3: +3, +9, +27, +81. The next is +243, giving 126 + 243 = 369.
What is the arithmetic mean (average) of 2,4, 6, 8,10 and 12?
The numbers are evenly spread, so the mean is the midpoint of 2 and 12, that is 7.
'A' has a brother 'B’. 'A' is son of 'C’. 'D' is father of 'C'. What relation is 'B' of ‘D'?
A is the son of C and D is the father of C, so D is A's grandfather. B is A's brother, so B is also D's grandson.
Complete the number series "3, 2, 7, 6, 11, _"?
The series interleaves 3, 7, 11 and 2, 6, 10, each rising by 4. The next term belongs to the second, giving 10.
Simplify: 18800/470/20?
Working left to right: 18,800 / 470 = 40, then 40 / 20 = 2.
If 25 toys cost 500, what would be the cost of 75 toys?
25 toys cost 500, so one costs 20. Seventy-five cost 75 x 20 = 1,500.
Imran made a profit of 20 percent in the first year. Next year he had a loss of 25 percent on the capital he had at the beginning of the second year. What was his overall loss?
A 20% gain then a 25% loss gives 1.20 x 0.75 = 0.90, so he ends with 90% of his capital, an overall loss of 10%.
What is the next term for the sequence 486, 162, 54, 18, 6…?
Each term is divided by 3: 486, 162, 54, 18, 6. The next is 6/3 = 2.
What is 0.004 x 0.5?
0.004 x 0.5 = 0.002.
About the PPSC Mathematics Past Paper 2016
Every MCQ above is taken from the Punjab Public Service Commission (PPSC) Mathematics papers held in 2016, 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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