SSC MTS 2021 PYQs

Question 1

An article was sold at 65% of its marked price, and thus there was a gain of 30%. Find the ratio of the marked price to cost price.

Accepted Answer

Let MP be 100. SP = 65% of MP = 65. Since there's a 30% gain, CP = SP / 1.30 = 65 / 1.3 = 50. The ratio MP:CP is 100:50, which simplifies to 2:1.

Question 2

A man sold a radio and a TV set together for Rs. 30,400. thereby making a profit of 25% on the radio and 10% on the TV set. By selling them together for Rs. 30,700, he would have made a 10% profit on the radio and 25% on the TV set. The cost price of the radio is:

Accepted Answer

Let R and T be the cost prices. Form two equations based on the given selling prices and profit percentages. Solve these simultaneous equations to find R and T. The cost price of the radio (R) will be Rs. 12,000.

Question 3

The internal and external diameters of a hollow hemispherical bowl are 18 cm and 22 cm, respectively. The total surface area (in cm2) of the bowl is:

Accepted Answer

Calculate the inner curved surface area (2πr²), outer curved surface area (2πR²), and the area of the top ring (πR² - πr²). Sum these three areas to get the total surface area.

Question 4

The area of a square is S, and that of the square formed by joining the mid-points of the given square is A, The value of‌ASis equal to:

Accepted Answer

When a square is formed by joining the mid-points of another square, its area is exactly half the area of the original square. Thus, A = S/2, so A/S = 1/2 = 0.5.

Question 5

Select the most appropriate meaning of the given idiom.Of the old school

Accepted Answer

The idiom 'of the old school' refers to someone who holds traditional or old-fashioned beliefs and values, especially regarding conduct or methods.

Question 6

X is 60% more efficient than Y, and Y alone can do a work in 80 days. Working together, X and Y will complete 52% of the same work in:

Accepted Answer

Y's 1-day work is 1/80. X is 60% more efficient, so X's 1-day work is 1.6 * (1/80) = 1/50. Together, they do (1/80 + 1/50) = 13/400 work per day. To complete 52% of work: (0.52) / (13/400) = 16 days.

Question 7

If the area of the base of a cylinder is 346.5cm2and the area of the curved surface is 990cm2, then its height is: (Take π =‌227)

Accepted Answer

From base area (πr² = 346.5), find radius r. Then use curved surface area (2πrh = 990) with the calculated r to find the height h. The height is 15 cm.

Question 8

The income of A is 50% more than that of B. If the income of A is increased by 40% and the income of B is increased by 30%, then the percentage increase in their combined income is:

Accepted Answer

Assume B's income is 100. A's income is 150. Combined income is 250. New A's income is 150*1.4 = 210. New B's income is 100*1.3 = 130. New combined income is 340. Percentage increase is ((340-250)/250)*100 = 36%.

Question 9

The cost price of 30 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:

Accepted Answer

Let CP of 1 article be Re 1. Total CP = 30. SP of x articles = 30. Profit = 25%. So, SP = CP * (1 + 0.25) = 30 * 1.25 = 37.5. Since SP of x articles = 30, and SP of 30 articles = 37.5, then x = 30 / 1.25 = 24.

Question 10

55% of the candidates in an examination were boys. 60% of the boys and 75% of the girls passed, and 315 girls failed. The number of boys who failed were:

Accepted Answer

Girls failed are 315, which is 25% of total girls. So total girls = 315 / 0.25 = 1260. Girls are 45% of total candidates, so total candidates = 1260 / 0.45 = 2800. Boys are 55% of 2800 = 1540. Boys failed = 40% of 1540 = 616.

Question 11

What is the sum of the numbers between 300 and 500 such that when they are divided by 6, 12 and 16, it leaves no remainder?

Accepted Answer

Find the LCM of 6, 12, 16, which is 48. Identify multiples of 48 between 300 and 500 (336, 384, 432, 480). Sum these numbers to get the final answer.

Question 12

A, B and C complete a work in 5 days, 8 days and 12 days, respectively. If they work together and get ₹ 9,800 for the work, then how much does A get?

Accepted Answer

Find the LCM of days (5, 8, 12) which is 120. Calculate individual efficiencies: A=24, B=15, C=10. Wages are distributed in this efficiency ratio. A's share = (24 / (24+15+10)) * 9800 = ₹ 4800.

Question 13

The number of students taking admission in First Year of a Degree Course at a college in areas of Social Sciences in 2012 was as follows: Economics (S1) - 96, Psychology (S2) - 84, History (S3) - 160. Political Science (S4) - 120. Sociology (S5) - 125. The break-up of students in different subjects has been presented through the given pie chart.Study the pie chart and answer the question that follows.In 2013, 20% of the Sociology students, 25% of the Political Science students, and one-sixth of the Economics students shifted to another college, and the number of History students got increased by 10% due to students shifting from other colleges. Over and above this, 10% of the remaining Sociology students and one-seventh of the Psychology students got transferred to Economics. What will be the central angle (to the nearest degree) of the sector corresponding to History in the pie chart, representing the break-up in 2013?

Accepted Answer

Calculate the total students in 2012 (96+84+160+120+125 = 585). Then, calculate the new number of students in each subject for 2013, considering all shifts. Find the new total. Finally, calculate the central angle for History: (New History students / New Total students) * 360.

Question 14

Select the most appropriate ANTONYM of the given word.SLEEK

Accepted Answer

Sleek means smooth and glossy. The most appropriate antonym is 'Dull', which means lacking brightness or luster, the opposite of glossy.

Question 15

If the radius of a cylinder is decreased by 40% and the height is increased by 60% to form a new cylinder, then the volume will be decreased by

Accepted Answer

Original volume V = πr²h. New radius r' = 0.6r, new height h' = 1.6h. New volume V' = π(0.6r)²(1.6h) = π(0.36r²)(1.6h) = 0.576πr²h. Percentage decrease = ((V - V')/V) * 100 = (1 - 0.576) * 100 = 42.4%.

Question 16

A car covers a distance of 450 km at a certain uniform speed (in km/h). The number of hours it takes for the journey is‌18of the number representing the speed. The time taken (in hours) by the car to cover the distance is:

Accepted Answer

Let speed be 's' and time be 't'. Given t = s/8 and distance = 450 km. Using distance = speed × time, substitute t = s/8 to get 450 = s × (s/8). Solve for s, then find t.

Question 17

What is the value of x, if (5 + 42) ÷ 3 of x – 2 × 4 = –7?

Accepted Answer

Using BODMAS, solve brackets and 'of' first: (5 + 16) ÷ 3x - 8 = -7. This gives 21 ÷ 3x = 1, so 3x = 21, which means x = 7.

Question 18

The values of the mode and median are 7.52 and 9.06, respectively, in a moderately asymmetrical distribution. The mean of the distribution is:

Accepted Answer

Use the empirical formula: Mode = 3 * Median - 2 * Mean. Substitute the given values: 7.52 = 3 * 9.06 - 2 * Mean. Solve for Mean: 2 * Mean = 27.18 - 7.52 = 19.66. Mean = 9.83.

Question 19

A fruit seller has a sale of Rs.10,435, Rs.9,927, Rs.10,855, Rs.10,230 and Rs.9,562 for five consecutive months. How much sale (in Rs.) must he have in the sixth month so that he gets an average sale of Rs.10,500?

Accepted Answer

The total target sale for 6 months is 6 * 10,500 = 63,000. The sum of sales for the first 5 months is 51,009. The required sale for the sixth month is 63,000 - 51,009 = 11,991.

Question 20

The numbers 25, 34, 46, 48, 2x+1, 4x+3, 105, 110, 114, 122 are written in ascending order and their median is 77. The value of x is:

Accepted Answer

There are 10 numbers. The median is the average of the 5th and 6th terms. So, (2x+1 + 4x+3)/2 = 77. Solving this equation gives 6x+4 = 154, leading to 6x = 150, and x = 25.