SSC MTS 2022 PYQs

Question 1

A man buys a toy for Rs. 400 and sells it at a loss of 15%. What is the selling price of the toy?

Accepted Answer

Calculate 15% of Rs. 400, which is Rs. 60. Subtract this loss from the cost price: 400 - 60 = Rs. 340. This is the selling price.

Question 2

The following pie-chart shows the sales in a restaurant in a day, in percentage terms.If the total number of items sold in a day is 100, then what is the central angle made by the sector giving data about the sale of 'Sandwich' in the pie-chart?

Accepted Answer

A full circle is 360 degrees. If 'Sandwich' sales are 20% of total, then the central angle is 20% of 360 degrees, which is (20/100) * 360 = 72 degrees.

Question 3

If 256, K, 81 are in proportion, and K is positive, then what is the value of K?

Accepted Answer

For numbers a, b, c to be in proportion, b² = ac. Here, K² = 256 × 81. So, K = √(256 × 81) = 16 × 9 = 144.

Question 4

The pie chart given below shows the number of laptops sold of each of 7 different brands in a year as percentages of the total number of laptops sold of all these 7 brands taken together in that year.What is the difference between the measures of the central angles made by sector B2 and sector B5?

Accepted Answer

Sector B2 is 15% and B5 is 11%. The difference is 4%. Central angle for 1% is 3.6°. So, 4% difference is 4 * 3.6° = 14.4°.

Question 5

5 men can complete a work in 12 days, and 6 women can complete the same work in 20 days. In how many days can 1 man and 1 woman together complete this work?

Accepted Answer

Calculate individual man's and woman's daily work rate. 1 man does 1/60 of work daily, 1 woman does 1/120. Together, they do (1/60 + 1/120) = 3/120 = 1/40 of work daily. So, they complete it in 40 days.

Question 6

S1and S2can do a piece of work together in 18 days, S2and S3can do the same work together in 27 days, while S3and S1can do it together in 54 days. In how many days can all 3, working together, do 50% of the work?

Accepted Answer

Calculate individual work rates. Sum their combined rates to find (S1+S2+S3)'s rate. Then, find the time to complete 50% of the work using this combined rate.

Question 7

Geeta bought a bag for Rs. 1,000 and spent Rs. 300 on fixing the defects in the bag. Later, she sold it for Rs. 1,508. What is the percentage of profit that Geeta earned through the sale?

Accepted Answer

Total cost price is 1000 + 300 = 1300. Profit is 1508 - 1300 = 208. Profit percentage = (208/1300) * 100 = 16%.

Question 8

What is the value of 	ext"‌511of‌"‌‌37+‌711×‌5521−‌822÷‌1633?

Accepted Answer

Apply BODMAS rule: first 'of', then multiplication/division from left to right, finally addition/subtraction. Simplify each term before combining to get the correct fraction.

Question 9

Find a single discount equivalent to two successive discounts of 12% and 8%.

Accepted Answer

Use the formula for successive discounts: A + B - (A*B)/100. Substitute 12 and 8 to get 12 + 8 - (12*8)/100 = 20 - 0.96 = 19.04%.

Question 10

The ratio of the length to the width of a rectangle is 3 ∶ 2. If the length of this rectangle is increased by 25% and its width is kept constant, then the area of the rectangle increases by 24 m2. What is the width of this rectangle?

Accepted Answer

Let length be 3x and width be 2x. New length is 3x * 1.25 = 3.75x. Original area = 6x^2, new area = 7.5x^2. Difference is 1.5x^2 = 24, so x^2 = 16, x = 4. Width = 2x = 8m.

Question 11

Karun borrowed Rs. 12,000 from Varun and Rs. 15,000 from Tarun, each for two years at the same rate of simple interest per annum. If he paid an interest of Rs. 1,680 to Varun at the end of 2 years, then what is the interest that Karun paid to Tarun at the end of the 2-year period?

Accepted Answer

First, calculate the interest rate using Varun's loan: Rate = (1680 * 100) / (12000 * 2) = 7%. Then, apply this rate to Tarun's loan: Interest = (15000 * 7 * 2) / 100 = Rs. 2100.

Question 12

In a week, the average temperature of Sunday and Monday is 37.2°C. The average temperature of Tuesday and Wednesday is 39.4°C. Find the temperature on Sunday if the average temperature of Monday, Tuesday and Wednesday is 38.1°C?

Accepted Answer

Let S, M, T, W be temperatures. S+M = 2*37.2 = 74.4. T+W = 2*39.4 = 78.8. M+T+W = 3*38.1 = 114.3. Substitute T+W into M+T+W: M+78.8 = 114.3, so M = 35.5. Then S+35.5 = 74.4, so S = 38.9°C.

Question 13

The radius of a sphere is 14 cm. What is the surface area of this sphere? [Use π =‌227]

Accepted Answer

The surface area of a sphere is given by the formula 4πr². Substitute r=14 cm and π=22/7 to get 4 * (22/7) * 14 * 14 = 2464 cm².

Question 14

The present ages of A and B are in the ratio 3 ∶ 5. If A’s present age is 33 years, then what will be B’s age (in years) after 5 years?

Accepted Answer

A's age is 33 years, which corresponds to 3 parts of the ratio. So, 1 part = 33/3 = 11 years. B's present age is 5 parts = 5 * 11 = 55 years. After 5 years, B's age will be 55 + 5 = 60 years.

Question 15

Simplify the following expression.12 + 11 - 13 + (4 + 3)

Accepted Answer

First, solve the parentheses: 4 + 3 = 7. Then, perform additions and subtractions from left to right: 12 + 11 = 23, 23 - 13 = 10, 10 + 7 = 17.

Question 16

A policeman spots a thief at a distance of 200 m and starts chasing him. While the policeman runs at a speed of 9 km/h, the thief runs at a speed of 7 km/h. After how long will the policeman catch the thief?

Accepted Answer

Relative speed is 9-7 = 2 km/h. Convert to m/s: 2 * (5/18) = 5/9 m/s. Time = Distance/Speed = 200 / (5/9) = 360 seconds = 6 minutes.

Question 17

G1can do a piece of work alone in 20 days, G2can do the same piece of work alone in 40 days, while G3can do it alone in 60 days. They worked together and completed the work. If the combined share received by G1and G2is Rs. 2,700, then what is the total amount received by all the 3 workers taken together?

Accepted Answer

Calculate the ratio of efficiencies (1/20 : 1/40 : 1/60 = 6:3:2). Wages are distributed in this ratio. If G1+G2 (6+3=9 parts) get Rs. 2700, then 1 part = Rs. 300. Total (6+3+2=11 parts) = 11 * 300 = Rs. 3300.

Question 18

What is the increase in the volume of a cube of 1 unit edge if each of its edges is tripled?

Accepted Answer

Original volume is 1³ = 1 cubic unit. New edge is 3 units, so new volume is 3³ = 27 cubic units. The increase in volume is 27 - 1 = 26 cubic units.

Question 19

If A = 3 + 7 × 2, B = 12 ÷ 4 - 6, and C = 6 × 5 + 2, then what is the value of A × B + C?

Accepted Answer

First, calculate A = 3 + 14 = 17. Then, B = 3 - 6 = -3. Next, C = 30 + 2 = 32. Finally, A × B + C = 17 × (-3) + 32 = -51 + 32 = -19.

Question 20

If Δ ABC is similar to Δ DEF such that BC = 3 cm, EF = 4 cm and the area of Δ ABC = 54 cm2, then the area of Δ DEF is:

Accepted Answer

For similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides. So, Area(ΔABC)/Area(ΔDEF) = (BC/EF)². Substitute values: 54/Area(ΔDEF) = (3/4)². Solve for Area(ΔDEF) = 54 * (16/9) = 96 cm².