SSC CHSL 2022 PYQs

Question 1

Ifk+(‌1k)=2, find the value of 8k × k × k

Accepted Answer

The given equation k + (1/k) = 2 implies k = 1. Substitute k=1 into 8k × k × k to get 8 × 1 × 1 × 1 = 8.

Question 2

A watercraft is rowed down 32 km along a river in 4 hours and 10 km against the river in 5 hours. Find the speed of the watercraft and that of the river.

Accepted Answer

Downstream speed = 32/4 = 8 km/h. Upstream speed = 10/5 = 2 km/h. Speed of watercraft = (8+2)/2 = 5 km/h. Speed of river = (8-2)/2 = 3 km/h.

Question 3

If a + b = 2c, then the value of‌aa−c+‌cb−cis:

Accepted Answer

From a + b = 2c, we can write a - c = c - b. Substitute this into the expression: a/(a-c) + c/(b-c) = a/(a-c) + c/(-(a-c)) = (a-c)/(a-c) = 1.

Question 4

If 2945 ÷ 19 – 11 × 5 = 29 + a, find the value of a.

Accepted Answer

First, perform division and multiplication: 2945 ÷ 19 = 155 and 11 × 5 = 55. The equation becomes 155 - 55 = 29 + a, which simplifies to 100 = 29 + a. Thus, a = 100 - 29 = 71.

Question 5

A shopkeeper wanted to sell ₹2,700 worth of products. But he had two options — giving two successive discounts of 10% and 15%, respectively, or giving a single discount of 25%. What was the difference between the two options?

Accepted Answer

Calculate the effective discount for successive discounts using the formula A+B - (AB/100). Then find the difference between this effective discount and the single discount of 25% on the original price.

Question 6

How many two-digit numbers are divisible by 3 or 5?

Accepted Answer

Two-digit numbers range from 10 to 99. Use the inclusion-exclusion principle: (divisible by 3) + (divisible by 5) - (divisible by 15). This gives 30 + 18 - 6 = 42.

Question 7

Rohan scored 70 and 75 marks in the first two tests. How many marks should he score in the third test to get an average of 70 marks?

Accepted Answer

The total marks needed for an average of 70 in three tests is 70 * 3 = 210. Rohan already scored 70 + 75 = 145. So, he needs 210 - 145 = 65 marks in the third test.

Question 8

The fourth proportional to 5, 8 and 30 is:

Accepted Answer

Let the fourth proportional be x. Then 5/8 = 30/x. Cross-multiply to get 5x = 8 * 30, so 5x = 240. Dividing by 5 gives x = 48.

Question 9

The average present age of four members of a family is 27 years and average increases by 3 years when one of their relatives joins them. The age of the relative is:

Accepted Answer

Initial total age = 4 * 27 = 108 years. After relative joins, total members = 5, new average = 27 + 3 = 30 years. New total age = 5 * 30 = 150 years. Relative's age = 150 - 108 = 42 years.

Question 10

A, B and C can do a work in 5 days,6 days and 10 days, respectively. Working together, in how many days will they finish the same work?

Accepted Answer

Calculate individual work rates (1/5, 1/6, 1/10). Sum these rates to find the combined rate (1/5 + 1/6 + 1/10 = 6+5+3/30 = 14/30 = 7/15). The total time is the reciprocal of the combined rate, which is 15/7 days or 2 1/7 days.

Question 11

If the curved surface area of a closed cylinder is 225 cm2and the area of its base is 169 cm2, then find the total surface area of the cylinder.

Accepted Answer

The total surface area of a closed cylinder is the sum of its curved surface area and twice the area of its base. So, 225 + 2 * 169 = 225 + 338 = 563 cm².

Question 12

There is a continuous growth in the population of a village at the rate of 5% per annum. If its present population is 18522, what was the population of the village 3 years ago?

Accepted Answer

Let the population 3 years ago be P. Using the compound growth formula, 18522 = P * (1 + 5/100)^3. Solving for P gives P = 18522 / (1.05)^3 = 18522 / 1.157625 = 16000.

Question 13

Roshni travelled at the speed of 66 km/h while going from point A to point B and returned via the same route at the speed of 92.4 km/h. What was Roshni's overall average speed during the two-way journey?

Accepted Answer

Use the formula for average speed when distance is constant: 2ab/(a+b). Substitute a=66 and b=92.4 to get 2 * 66 * 92.4 / (66 + 92.4) = 77 km/h.

Question 14

Find the volume of the cuboid, if its length is thrice its breadth and its breadth is 8 cm, which is twice its height.

Accepted Answer

Given breadth = 8 cm. Height = breadth/2 = 4 cm. Length = 3 * breadth = 24 cm. Volume = length * breadth * height = 24 * 8 * 4 = 768 cm³.

Question 15

If 15 kg of sugar cost ₹600, what is the cost of 25 kg of sugar?

Accepted Answer

First, find the cost of 1 kg sugar by dividing ₹600 by 15 kg, which is ₹40/kg. Then, multiply ₹40 by 25 kg to get ₹1,000.

Question 16

On dividing 8675123 by a certain number, the quotient is 33611 and the remainder is 3485. The divisor is ______.

Accepted Answer

Using the division algorithm, Dividend = Divisor × Quotient + Remainder. Substitute the given values: 8675123 = Divisor × 33611 + 3485. Solve for Divisor: (8675123 - 3485) / 33611 = 8671638 / 33611 = 258.

Question 17

Harsh purchased a scooter for ₹48,000. He sold it at a loss of 15%. With that money he purchased another scooter and sold it at a profit of 22.5%. What is his overall loss/profit percentage?

Accepted Answer

Calculate the selling price after 15% loss, then calculate the selling price of the second scooter after 22.5% profit. Find the overall profit/loss percentage relative to the initial cost.

Question 18

If x2+ 4y2= 40, xy = 6 and x > 2y then the value of x - 2y is:

Accepted Answer

Use the identity (x - 2y)² = x² + 4y² - 4xy. Substitute the given values: (x - 2y)² = 40 - 4(6) = 40 - 24 = 16. Since x > 2y, x - 2y must be positive, so x - 2y = √16 = 4.

Question 19

In an engineering institution, a student’s grade is assessed based on Internal tests (30%), assignments (30%) and external exams (40%). If a student scored 90% in internal tests, 95% in assignments and 75% in external exams, then the overallgrade of the student is:

Accepted Answer

Calculate the weighted average: (90% * 0.30) + (95% * 0.30) + (75% * 0.40) = 27 + 28.5 + 30 = 85.5%. This is the overall grade.

Question 20

Number B is 17.5% less than number A, while number C is 22.5% more than number B. If the value of C is given as 8085, what is the value of A?

Accepted Answer

Given C = 8085 and C = B * (1 + 22.5/100) = 1.225B. So, B = 8085 / 1.225 = 6600. Also, B = A * (1 - 17.5/100) = 0.825A. Thus, A = 6600 / 0.825 = 8000.