SSC CHSL 2022 PYQs

Question 1

IfX−‌1x=11and x > 0, what is the value of(x2−‌1x2)?

Accepted Answer

We need to find (x^2 - 1/x^2) which is (x - 1/x)(x + 1/x). Given (x - 1/x) = 11. Calculate (x + 1/x) using (x + 1/x)^2 = (x - 1/x)^2 + 4. So, (x + 1/x) = sqrt(11^2 + 4) = sqrt(125) = 5sqrt(5). Multiply 11 * 5sqrt(5) to get 55sqrt(5).

Question 2

In a 1200 m race, the ratio of the speeds of two contestants Meenal and Nitu is 5 ∶ 7. If Meenal has a start of 500 m, then Meenal wins by:

Accepted Answer

Meenal runs 1200 - 500 = 700m. Nitu runs 7/5 * 700 = 980m in the same time. Meenal wins by 1200 - 980 = 220m.

Question 3

If (x + 2) and (x − 3) are the factors of x2+ k1x + k2, then:

Accepted Answer

Since (x+2) and (x-3) are factors, the polynomial is (x+2)(x-3) = x² - x - 6. Comparing with x² + k₁x + k₂, we get k₁ = -1 and k₂ = -6.

Question 4

The area of a triangle is 96 cm2and the length of one of its sides is 24 cm. What is the length of the perpendicular drawn to this side of the triangle from the opposite vertex?

Accepted Answer

Use the formula for the area of a triangle: Area = (1/2) × base × height. Substitute the given values: 96 = (1/2) × 24 × height. Solve for height to get 8 cm.

Question 5

The population of a city increases by 10% annually. If its present population is 21,000, what will be the population in 3 years?

Accepted Answer

Use the compound growth formula: P(1 + r/100)^n. Substitute P=21000, r=10, n=3. Calculate 21000 * (1.1)^3 = 21000 * 1.331 = 27951.

Question 6

If the sum of two numbers is 25 and their product is 144, then what is the position difference between the two numbers?

Accepted Answer

Let the numbers be x and y. We have x+y=25 and xy=144. Use the identity (x-y)² = (x+y)² - 4xy. Substitute the values to find (x-y)² = 25² - 4*144 = 625 - 576 = 49. Thus, x-y = √49 = 7.

Question 7

Study the given graph carefully and answer the question that follows.In which of the following years was the sales of company 1 exactly half of the total sales of companies 2 and 3 together in that year?

Accepted Answer

Check each year: In 2016, Company 1 sales were 200, and Company 2 + 3 sales were 150 + 250 = 400. Since 200 is half of 400, 2016 is the correct year.

Question 8

If[3‌67‌÷‌‌547‌−‌{3‌−‌(2‌34‌−‌‌32)}]‌+ A ÷ 4 = 0, then what is the value of A?

Accepted Answer

Simplify the expression using BODMAS. First, solve the innermost bracket: (2 3/4 - 3/2) = (11/4 - 3/2) = 5/4. Then, 3 - 5/4 = 7/4. Next, 36/7 ÷ 54/7 = 36/7 * 7/54 = 36/54 = 2/3. So, 2/3 - 7/4 = (8-21)/12 = -13/12. Finally, -13/12 + A/4 = 0, which gives A/4 = 13/12, so A = 13/3.

Question 9

If x ∶ y = 1 ∶ 2, find the value of (2x + 4y) ∶ (x + 4y).

Accepted Answer

Substitute x=1 and y=2 into the expression (2x + 4y) : (x + 4y). This gives (2*1 + 4*2) : (1 + 4*2) = (2+8) : (1+8) = 10 : 9.

Question 10

Air is pumped into a spherical balloon, its radius increases from 7 cm to 14 cm. Find the ratio of volume of the balloon's in both circumstances.

Accepted Answer

The volume of a sphere is (4/3)πr³. When the radius doubles from 7 cm to 14 cm, the volume ratio becomes (7³):(14³) = 1³:2³ = 1:8.

Question 11

The price of a tablet is first increased by 10%, and then decreased by 2.5% due to reduction in sales. What is the net percentage change in the final price of the tablet?

Accepted Answer

Assume initial price is 100. After 10% increase, price is 110. After 2.5% decrease on 110, price is 107.25. Net change is 107.25 - 100 = 7.25% increase.

Question 12

What should be subtracted from 246837 to make it divisible by 13 ?

Accepted Answer

Divide 246837 by 13. The remainder is 6. To make the number divisible by 13, subtract this remainder from the original number.

Question 13

The ratio of the cost price to the marked price of an article is 4 ∶ 7. A discount of 25% is given on the marked price and the shopkeeper made a profit of ₹50. Find the cost price of the article.

Accepted Answer

Let CP be 4x and MP be 7x. Selling Price (SP) = 7x * (1 - 0.25) = 5.25x. Profit = SP - CP = 5.25x - 4x = 1.25x. Given profit is ₹50, so 1.25x = 50, which means x = 40. Cost Price = 4x = 4 * 40 = ₹160.

Question 14

The tax on a commodity diminishes by 14% and its consumption increases by 10%. Find the effect on revenue.

Accepted Answer

Revenue = Tax × Consumption. A 14% decrease in tax (0.86) and a 10% increase in consumption (1.10) results in 0.86 × 1.10 = 0.946. This is a 5.4% decrease, which rounds to 5.5%.

Question 15

In a right circular cone, the radius of the base is 14 cm and the height is 48 cm. A cross-section is made through the midpoint of the height parallel to the base. The volume of the upper portion is: (Take π = 22/7)

Accepted Answer

The upper portion is a smaller cone with half the original height and radius. Calculate its volume using V = (1/3)πr²h. Substitute r=7cm, h=24cm to get 1232 cm³.

Question 16

Find the value of(‌93‌+‌94‌+‌95‌+‌96‌+‌9791+92+93+94+95)‌12.

Accepted Answer

Factor out 9^3 from the numerator and 9^1 from the denominator. Simplify the common terms in the parentheses. The expression reduces to (9^2)^1/2, which is 9.

Question 17

A motorcycle covers 50 km at a speed of 25 km/h. Find the speed of the motorcycle for the next 50 km of the journey so that the average speed of the whole journey will be 30 km/h.

Accepted Answer

Total distance is 100 km. Total time = Total distance / Average speed = 100/30 hours. Time for first 50 km = 50/25 = 2 hours. Time for next 50 km = (100/30) - 2 = 4/3 hours. Speed = 50 / (4/3) = 37.5 km/h.

Question 18

A can do a piece of work in 24 days and B can do it in 80 days. B works alone for 2 days and A works alone on the 3rdday. This process continues till the work is completed. In how many days will the work be completed?

Accepted Answer

Calculate individual daily work rates. Find work done in one 3-day cycle (B+B+A). Divide total work by cycle work to find cycles, then add remaining days.

Question 19

In a company there are only two types of employees, workers and officers. 35% of the employees are officers and the average monthly salary of an officer is ₹39,000 more than the combined average monthly salary of an employee. What is the difference between the average monthly salaries of an officer and a worker?

Accepted Answer

Let total employees be 100. Officers = 35, Workers = 65. Let combined average salary be A. Officer's average salary = A + 39000. Using weighted average formula, calculate worker's average salary and then find the difference.

Question 20

How many 25 cm × 11.25 cm × 6 cm bricks will be required to construct an 8 m × 6 m × 22.5 cm wall? (ignoring other material used)

Accepted Answer

First, convert all dimensions to the same unit (cm). Calculate the volume of the wall and one brick. Divide the wall's volume by the brick's volume to find the number of bricks needed.