SSC MTS 2019 PYQs

Question 1

The sum of the two numbers is 77 and their ratio is 6 : 5. What is their difference?

Accepted Answer

Let the numbers be 6x and 5x. Their sum is 11x = 77, so x = 7. Their difference is 6x - 5x = x = 7.

Question 2

The radius of a right circular cone and a right circular cylinder are in the ratio 2 : 3. If the ratio of the height of the cone and the cylinder is 3 : 4, then what is the ratio of the volume of the cone and the cylinder?

Accepted Answer

Let radii be 2r and 3r, heights 3h and 4h. Volume of cone = (1/3)π(2r)²(3h) = 4πr²h. Volume of cylinder = π(3r)²(4h) = 36πr²h. Ratio = 4πr²h : 36πr²h = 1 : 9.

Question 3

Pipe A can fill a tank in 6 hours. Pipe B can fill the same tank in 8 hours. Pipe A, B and C together can fill the same tank in 12 hours. Then which of the following statements is true for pipe C?

Accepted Answer

Pipe A fills 1/6, B fills 1/8. A+B+C fill 1/12. C's rate = (1/12) - (1/6 + 1/8) = (2-4-3)/24 = -5/24. Negative rate means C empties the tank in 24/5 hours = 4 hours 48 minutes.

Question 4

The perimeter of a rhombus is 20 cm. The length of one of its diagonals is 6 cm. What is the length of the other diagonal?

Accepted Answer

A rhombus has four equal sides. Perimeter 20 cm means each side is 5 cm. Diagonals bisect each other at 90 degrees. Using Pythagoras theorem on the right triangle formed by half-diagonals and a side, the other half-diagonal is 4 cm, so the full diagonal is 8 cm.

Question 5

What is the smallest number which when increased by 5 is divisible by 12, 18 and 30?

Accepted Answer

Find the LCM of 12, 18, and 30, which is 180. Since the number increased by 5 is divisible, subtract 5 from the LCM. So, 180 - 5 = 175.

Question 6

A, B, and C, working alone can do a piece of work in 15, 30 and 75 days respectively. They work together and get Rs. 1615 for completing the work. What is the difference in shares of A and C?

Accepted Answer

Calculate the efficiency ratio of A:B:C as 1/15 : 1/30 : 1/75 = 10:5:2. Total shares are 17. A's share is (10/17)*1615 = 950. C's share is (2/17)*1615 = 190. Difference is 950 - 190 = 760.

Question 7

Pipe A can completely fill an empty tank in 11 hours. Pipe B can empty the same completely filled tank in 15 hours. If they are opened together, in how much time the empty tank will get filled?

Accepted Answer

Pipe A fills 1/11 of the tank per hour, Pipe B empties 1/15 per hour. Combined rate is (1/11 - 1/15) = 4/165. So, the tank fills in 165/4 hours, which is 41 hours 15 minutes.

Question 8

The monthly incomes of A and B are in the ratio 3 : 4 and the ratio of their monthly expenditures is 2 : 3. If each saves Rs. 4000 per month, then what is the income of B?

Accepted Answer

Let incomes be 3x, 4x and expenditures 2y, 3y. Income - Expenditure = Savings. So, 3x - 2y = 4000 and 4x - 3y = 4000. Solving these equations gives x = 4000. B's income is 4x = 16000.

Question 9

The difference in selling price of an article when it is sold at 20% profit and 18% loss is Rs 570. If it is sold at 12% loss, then what will be the selling price of the article?

Accepted Answer

Let CP be x. Difference in SP is (1.20x - 0.82x) = 0.38x = 570. So, x = 1500. Selling price at 12% loss is 1500 * 0.88 = 1320.

Question 10

If A = 8 ÷ 4 × (3 - 1) + 6 × 3 ÷ 2 of 3 and B = 4 ÷ 8 × 2 + 7 × 3, then what is the value of A + B?

Accepted Answer

Calculate A using BODMAS: A = 8 ÷ 4 × 2 + 6 × 3 ÷ 6 = 2 × 2 + 18 ÷ 6 = 4 + 3 = 7. Calculate B: B = 0.5 × 2 + 21 = 1 + 21 = 22. So, A + B = 7 + 22 = 29.

Question 11

If the height of an equilateral triangle is 20√2 cm, then what is its area (in cm‌2)?

Accepted Answer

The height of an equilateral triangle is (√3/2)a. Given height is 20√2. So, a = 40√2/√3. Area = (√3/4)a² = (√3/4) * (1600*2/3) = (√3/4) * (3200/3) = 800√3/3 cm².

Question 12

By selling an article for Rs. 320, a man incurs a loss of 20%. What should be the selling price of an article to gain 20%?

Accepted Answer

If 320 Rs is 80% of CP (100%-20% loss), then CP = 320/0.8 = 400 Rs. To gain 20%, SP = 400 * 1.2 = 480 Rs.

Question 13

A car can travel a distance of 300 meters in 6 minutes. What is its average speed in km/h?

Accepted Answer

Convert distance to km (0.3 km) and time to hours (0.1 hours). Speed = Distance/Time = 0.3 km / 0.1 h = 3 km/h.

Question 14

Pipe P can fill a tank alone in 7 hours. Pipe Q can fill the same tank alone in 13 hours. In how much time can they together fill the tank?

Accepted Answer

Pipe P fills 1/7 of the tank per hour, Q fills 1/13. Together, their rate is (1/7 + 1/13) = 20/91. So, they fill the tank in 91/20 hours, which is 4.55 hours or 4 hours 33 minutes.

Question 15

What is the value of 90 × 3 ÷ 9 + 4 ÷ 2 × 3 of 4 × 8 ÷ (18 × 2 – 4)?

Accepted Answer

Apply BODMAS rule: First solve brackets (18×2-4 = 32), then 'of' (3 of 4 = 12). Then multiplication/division from left to right, followed by addition. This yields 30 + 12 = 42.

Question 16

A sold an article for Rs. 1495 at a profit of 15%. He purchased another article having cost price equal to the previous article. He sold this new article at a profit of 10%. How much total profit has A earned?

Accepted Answer

First, find the cost price of the first article (1495 / 1.15 = 1300). Profit on the first is 195. The second article's cost is also 1300, with a 10% profit (130). Total profit is 195 + 130 = 325.

Question 17

A is 20% more than B. B is 25% more than C. C is how much percent less than A?

Accepted Answer

Assume C = 100. Then B = 125 (25% more than C). A = 125 * 1.20 = 150 (20% more than B). C is (150-100)/150 * 100 = 33.33% less than A.

Question 18

What is the Highest Common Factor of716,2132‌and‌498?

Accepted Answer

The question asks for the Highest Common Factor (HCF) of 716, 2132, and 498. The numbers provided in the options are not standard HCF values. This is a trick question; the numbers are actually powers of 7. The HCF of 7^16, 7^32, and 7^98 is 7^16.

Question 19

26% of A = 832. What is the value of 31% of A?

Accepted Answer

First, find A by dividing 832 by 0.26, which gives A = 3200. Then, calculate 31% of 3200 by multiplying 3200 by 0.31, resulting in 992.

Question 20

A train, 700 m long crosses a pole in 35 seconds. How much time does it take to cross a platform of length 740 m?

Accepted Answer

First, calculate the train's speed using its length and time to cross a pole (Speed = Distance/Time). Then, for crossing the platform, the total distance is the train's length plus the platform's length. Use this total distance with the calculated speed to find the new time.