SSC MTS 2024 PYQs

Question 1

Surendra bought an old bicycle for ₹2,500 and spent ₹300 on its repair. He sold it for ₹3,000. Find his profit percentage.

Accepted Answer

Total cost price is ₹2500 (purchase) + ₹300 (repair) = ₹2800. Profit is ₹3000 - ₹2800 = ₹200. Profit percentage = (200/2800) * 100 = 7.14% or 7 1/7%.

Question 2

A hemispherical bowl with diameter 14 cm has to be painted inside and outside. How much it will be charged at the rate of ₹20 per 40 cm²?

Accepted Answer

The diameter is 14 cm, so the radius is 7 cm. The total surface area to be painted (inside + outside) is 2 * (2πr²) = 4πr². Calculate this area, then multiply by the rate (₹20/40 cm²).

Question 3

A chemist prepares 100 grams of medicine by mixing two ingredients X and Y. The rate of X is ₹1,500 per 100 grams and that of Y is ₹50 per 10 grams. X and Y are mixed in such a way that the cost of the resulting medicine is ₹13 per gram. What is the quantity of X (in grams) in the medicine?

Accepted Answer

Convert rates to per gram: X = ₹15/g, Y = ₹5/g. The mixture costs ₹13/g. Using the allegation rule, the ratio of X:Y is (13-5) : (15-13) = 8:2 = 4:1. Total 100g, so X = (4/5)*100 = 80g.

Question 4

If 40% of A is equal to 64% of B, then what will be A : B?

Accepted Answer

Set up the equation 0.40A = 0.64B. Divide both sides by B and by 0.40 to get A/B = 0.64/0.40 = 64/40. Simplify the fraction by dividing by 8 to get 8/5, so A:B = 8:5.

Question 5

What sum (in ₹) will earn a simple interest of ₹240 in 4 years at 12% per year rate of interest?

Accepted Answer

Use the simple interest formula: SI = (P * R * T) / 100. Substitute SI=240, R=12, T=4 to find P. P = (240 * 100) / (12 * 4) = 24000 / 48 = 500.

Question 6

Study the given graph and answer the question that follows.The graph shows the sales of three products: P, Q and R by four companies: A, B, C and D.How much more in percentage is the total sales of R than total sales of P (rounded off to one decimal place)?

Accepted Answer

Calculate total sales for P and R. P = 100+120+110+130 = 460. R = 130+150+140+160 = 580. Percentage increase = ((580-460)/460)*100 = (120/460)*100 = 26.08%, which rounds to 26.1%.

Question 7

Find the simple interest (in ₹) on ₹2500 as a sum borrowed at 9% per year rate of interest for 6 years.

Accepted Answer

Use the formula SI = (P * R * T) / 100. Substitute P=2500, R=9, T=6. Calculate (2500 * 9 * 6) / 100 = 1350.

Question 8

Find the simple interest (in ₹) on ₹4000 as a sum borrowed at 4% per year rate of interest for 3 years.

Accepted Answer

Use the simple interest formula: SI = (P * R * T) / 100. Substitute P=4000, R=4, T=3 to get (4000 * 4 * 3) / 100 = 480.

Question 9

The radius of a solid right circular cone is 65 cm and its height is 72 cm. The total surface area (in cm2) of the cone is (use π = 22/7):

Accepted Answer

First, calculate the slant height (l) using Pythagoras theorem: l = sqrt(r^2 + h^2). Then, use the formula for total surface area of a cone: TSA = πr(r + l). Substitute values and simplify.

Question 10

How much sugar at ₹68/kg should be added to 20 kg of tea worth ₹440/kg so that the mixture be worth ₹130/kg?

Accepted Answer

Use the rule of allegation. The ratio of sugar to tea is (440-130) : (130-68) = 310 : 62 = 5 : 1. Since tea is 20 kg, sugar is 5 * 20 = 100 kg.

Question 11

Two mixers and one TV cost ₹7,000, while two TVs and one mixer cost ₹9,800. The value of one TV is:

Accepted Answer

Form two linear equations: 2M + T = 7000 and M + 2T = 9800. Multiply the second equation by 2 and subtract the first to find T. T = ₹4,200.

Question 12

A 725 m long train passes through a 235 m long tunnel in 48 sec. Find the speed of the train.

Accepted Answer

Total distance covered is the sum of train length and tunnel length (725 + 235 = 960 m). Speed = Distance/Time = 960m / 48s = 20 m/s. Convert to km/h by multiplying by 18/5, which gives 72 km/h.

Question 13

A hemispherical bowl is 264 cm round at the brim. Suppose that the bowl is half-full of beverage. If the beverage is served in hemispherical glasses 6 cm in the diameter at the top, how many people would be served?

Accepted Answer

First, find the radius of the bowl from its circumference. Calculate the bowl's half-volume. Then, find the volume of one small glass. Divide the bowl's half-volume by the glass's volume to get the number of servings.

Question 14

The radius of a cylinder is doubled due to which the volume of the new cylinder also gets doubled. The height of the new cylinder is what percentage of the old cylinder?

Accepted Answer

Let original radius be r, height h. Volume V = πr²h. New radius 2r, new volume 2V. So, 2V = π(2r)²h' = 4πr²h'. Thus, 2πr²h = 4πr²h', implying h' = h/2. So, new height is 50% of old height.

Question 15

Find the LCM of 1/7, 2/5, and 3/15.

Accepted Answer

To find the LCM of fractions, calculate the LCM of the numerators (1, 2, 3) which is 6, and the HCF of the denominators (7, 5, 15) which is 1. The LCM of fractions is LCM(numerators)/HCF(denominators) = 6/1 = 6.

Question 16

The radius of the base and height of a right circular cone are in the ratio 8 : 15. Find the slant height of the cone if its volume is 1005‌57cm3

Accepted Answer

Let radius r=8x, height h=15x. Volume = (1/3)πr²h. Substitute values and solve for x. Then calculate slant height l = √(r²+h²).

Question 17

Refer to the given table and answer the question that follows.YearCompany's % profit201730201810201920202015202125What was the revenue of the company if its expenditure was ₹600 crores in the year when its percentage profit was the maximum?

Accepted Answer

Maximum profit percentage is 30% in 2017. Profit = 30% of Expenditure = 0.30 * 600 = 180 crores. Revenue = Expenditure + Profit = 600 + 180 = 780 crores.

Question 18

A shopkeeper makes a 15% profit on a sale. He would have made 18%, if he had sold it for Rs.18 more. The cost price of the article is:

Accepted Answer

The difference in profit percentage (18% - 15% = 3%) corresponds to Rs.18. So, 3% of Cost Price = Rs.18. Calculate 100% of Cost Price: (18/3) * 100 = Rs.600.

Question 19

The highest common factor of 84 and 108 is:

Accepted Answer

Find the prime factors of 84 (2² × 3 × 7) and 108 (2² × 3³). The HCF is the product of common prime factors raised to the lowest power, which is 2² × 3 = 12.

Question 20

The average of seven consecutive numbers is 95. Find the middle number in the series of seven consecutive numbers.

Accepted Answer

For any series of consecutive numbers, the average is always the middle number. Thus, the middle number is 95.