SSC MTS 2023 PYQs

Question 1

What is the smallest integer that is divisible by 12, 22 and 32?

Accepted Answer

To find the smallest integer divisible by 12, 22, and 32, calculate their Least Common Multiple (LCM). The LCM of 12, 22, and 32 is 1056.

Question 2

What will be the LCM of 37, 41?

Accepted Answer

Since 37 and 41 are both prime numbers, their LCM is simply their product. Multiply 37 by 41 to get 1517.

Question 3

Jaya invested Rs. 14800 at 8.5% per annum on simple interest. The interest earned after 6 months is:

Accepted Answer

Use the simple interest formula: SI = (P * R * T) / 100. Here, P=14800, R=8.5%, and T=6 months = 0.5 years. Calculate SI = (14800 * 8.5 * 0.5) / 100 = 629.

Question 4

Three metal rods of length 77 cm, 110 cm and 121 cm are to be cut into parts of equal length. Each part must be as long as possible. What is the maximum number of pieces that can be cut?

Accepted Answer

Find the HCF of 77, 110, and 121, which is 11 cm. Then, divide each rod's length by 11 and sum the results: (77/11) + (110/11) + (121/11) = 7 + 10 + 11 = 28 pieces.

Question 5

30 percent of marked price is equal to 50 percent of cost price. If no discount is given, then what will be the profit percentage?

Accepted Answer

Let MP be marked price and CP be cost price. Given 0.30 MP = 0.50 CP, so MP/CP = 5/3. If no discount, SP=MP. Profit = MP-CP = 5-3 = 2. Profit % = (2/3)*100 = 66.67%.

Question 6

A man alone can paint a house in 9 day and a woman alone can paint the house in 18 days. If 3 men and 3 women worked together. then in how many day they will paint the house?

Accepted Answer

A man's 1-day work is 1/9, a woman's is 1/18. 3 men and 3 women's combined 1-day work is 3*(1/9) + 3*(1/18) = 1/3 + 1/6 = 1/2. So, they complete the work in 2 days.

Question 7

If the circumference of a circle is 13.2 cm, then what is its radius?

Accepted Answer

The circumference formula is C = 2πr. Given C = 13.2 cm, substitute and solve for r: 13.2 = 2 * (22/7) * r, which gives r = 2.1 cm.

Question 8

The length and breadth of a rectangle are increased by 25% and 32%, respectively. The percentage increase in the area of the resulting rectangle will be:

Accepted Answer

Let original length be L and breadth B. New length is 1.25L and new breadth is 1.32B. New area = 1.25L * 1.32B = 1.65LB. Percentage increase = (1.65 - 1) * 100 = 65%.

Question 9

A water purifier is on sale for 10% discount on the original price. A store- wide sale results in an additional discount of 15%. What is the total discount on the original price?

Accepted Answer

Assume original price is 100. After 10% discount, price is 90. An additional 15% discount on 90 is 13.5. Total discount is 10 + 13.5 = 23.5%.

Question 10

On selling an article for Rs. 329, a dealer lost 6%. The cost price of the article is

Accepted Answer

If selling price (SP) is Rs. 329 and loss is 6%, then SP = CP - 6% of CP = 94% of CP. So, CP = 329 / 0.94 = Rs. 350.

Question 11

Find the area of the rhombus whose diagonals are 16 cm and 20 cm.

Accepted Answer

The area of a rhombus is half the product of its diagonals. Given diagonals are 16 cm and 20 cm. Area = (1/2) * 16 * 20 = 160 cm².

Question 12

If the radius of a sphere is 35 cm, then what is the total surface area of ​​the sphere?

Accepted Answer

The total surface area of a sphere is given by 4πr². Substitute r=35 cm to get 4 * (22/7) * 35 * 35 = 15400 cm².

Question 13

The table given below shows the marked price and the value of discount of five different articles.ArticleMarked priceDiscountARs. 350Rs. 70BRs. 650Rs. 75CRs. 450Rs. 66DRs. 750Rs. 72ERs. 850Rs. 80Selling price = Marked price - DiscountL1 = The value of the average discount of articles C and D.L2 = Sum of the selling price of all articles.Find L2 + L1?

Accepted Answer

Calculate L1 as the average discount of C and D: (66+72)/2 = 69. Calculate L2 by summing (Marked Price - Discount) for all articles. L2 = (350-70) + (650-75) + (450-66) + (750-72) + (850-80) = 280 + 575 + 384 + 678 + 770 = 2687. Finally, L1 + L2 = 69 + 2687 = 2756.

Question 14

A man buys 21 mangoes for a rupee. How many mangoes had he sold for a rupee so that there is a loss of 30 percent?

Accepted Answer

Cost price of 21 mangoes is Re 1. To incur a 30% loss, the selling price should be 70% of the cost price. So, 21 mangoes should be sold for Re 0.70. To find how many mangoes for Re 1, divide 21 by 0.70, which is 30.

Question 15

Find the compound interest (CI) on Rs. 12,600 for 2 years at 10% per annum compounded annually.

Accepted Answer

Calculate the amount using A = P(1 + R/100)^T. A = 12600(1 + 10/100)^2 = 12600 * (1.1)^2 = 12600 * 1.21 = 15246. CI = A - P = 15246 - 12600 = 2646.

Question 16

By how much percentage is‌34thof 32 is lesser than‌46thof 96?

Accepted Answer

Calculate (3/4)*32 = 24 and (4/6)*96 = 64. The difference is 64-24=40. Percentage less = (40/64)*100 = 62.50%.

Question 17

Find the value of given expression.[76 – {90 ÷ 5 ⨯ (24 – 36 ÷ 3) ÷ 3}]

Accepted Answer

Apply BODMAS: First solve innermost bracket (24 - 12 = 12). Then {90 ÷ 5 × 12 ÷ 3} = {18 × 12 ÷ 3} = {216 ÷ 3} = 72. Finally, 76 - 72 = 4.

Question 18

A mixture contains liquid A and liquid B in the ratio of 5 : 4. If 2 litres of liquid B is added to it, then the ratio of liquid A and liquid B becomes 7 : 6. What is the quantity (in litres) of liquid A in the mixture?

Accepted Answer

Let initial quantities be 5x and 4x. After adding 2L of B, the ratio becomes 5x / (4x+2) = 7/6. Solve for x: 30x = 28x + 14, so 2x = 14, x = 7. Quantity of A is 5x = 5 * 7 = 35 litres.

Question 19

A filling pipe can fill a pot in 40 minutes and wastage pipe can empty the filled pot in 60 minutes. By mistake without closing the wastage pipe, the filling pipe opened. In how much time an empty pot can be filled?

Accepted Answer

The filling pipe's rate is 1/40 per minute, and the emptying pipe's rate is 1/60 per minute. When both operate, the net filling rate is (1/40 - 1/60) = 1/120 per minute. Thus, the pot fills in 120 minutes.

Question 20

A train moves at a speed of 30 m/s and crosses a bridge of length 650 metres in 50 seconds. What is the length of the train?

Accepted Answer

Total distance covered = speed × time = 30 m/s × 50 s = 1500 m. This distance is train length + bridge length. So, train length = 1500 m - 650 m = 850 m.