SSC CHSL 2024 PYQs

Question 1

Two quantities are in the ratio 3 : 5. If the first quantity is 155 kg. Find the other quantity (approximately).

Accepted Answer

Let the quantities be 3x and 5x. Given 3x = 155 kg, so x = 155/3. The other quantity is 5x = 5 * (155/3) = 775/3 = 258.33 kg (approximately).

Question 2

If a circle whose centre is (2, 3) touches the line 4x + 3y - 7 = 0, then the radius of the circle is:

Accepted Answer

The radius of the circle is the perpendicular distance from its center (2, 3) to the tangent line 4x + 3y - 7 = 0. Use the point-to-line distance formula: |Ax₀ + By₀ + C| / √(A² + B²).

Question 3

A policeman starts chasing a thief who is 500 m ahead of him. The speed of the thief is 18 km/h, and the speed of the policeman is 36 km/h. Find the time taken by the policeman to catch the thief.

Accepted Answer

Calculate the relative speed (36-18 = 18 km/h). Convert it to m/s (18 * 5/18 = 5 m/s). Time = Distance/Speed = 500m / 5m/s = 100 seconds.

Question 4

A shopkeeper decides to raise the marked price of an article by 40%. How much percentage discount should he allow to be able to sell the article at the original marked price?

Accepted Answer

Let original MP be 100. New MP is 140. To sell at original MP (100), discount needed is 40 on 140. Percentage discount = (40/140) * 100 = 28 (4/7)%.

Question 5

The price of an electric bike was Rs. 1,25,000 last year. This year, its price got decreased by 30%. What is the price (in Rs.) of the electric bike this year?

Accepted Answer

Calculate 30% of 1,25,000, which is 37,500. Subtract this decrease from the original price: 1,25,000 - 37,500 = 87,500.

Question 6

If A ∶ B = 3 ∶ 7 and B ∶ C = 2 ∶ 5, find A ∶ B ∶ C.

Accepted Answer

To combine ratios A:B and B:C, make the common term 'B' equal. Multiply A:B by 2 and B:C by 7 to get A:B:C = 6:14:35.

Question 7

The capacity of a cylinder tank is 8316 cm3. If the radius of its base is 21 cm, then find the depth of the tank.

Accepted Answer

Use the cylinder volume formula V = πr²h. Substitute V=8316 and r=21. Calculate h = 8316 / (π * 21²). This yields h = 6 cm.

Question 8

The simple interest on a sum of money for1‌12years at 10% per annum is Rs. 30 more than the simple interest on the same sum for 1 year at 12% per annum. Find the sum.

Accepted Answer

Let the sum be P. Set up the equation: (P * 1.5 * 10/100) - (P * 1 * 12/100) = 30. Simplify to 0.15P - 0.12P = 30, which gives 0.03P = 30. Solve for P = 1000.

Question 9

If the diameter of a hemisphere is 42 cm, then the volume of hemisphere (in cm3) is: Take π = 22/7

Accepted Answer

The diameter is 42 cm, so the radius is 21 cm. Use the formula for the volume of a hemisphere: (2/3)πr³. Substitute r=21 and π=22/7 to get 19404 cm³.

Question 10

Among the ratios 3 : 4, 5 : 8, 1 : 2, 6 : 9 which is the greatest?

Accepted Answer

Convert each ratio to a decimal: 3/4 = 0.75, 5/8 = 0.625, 1/2 = 0.5, 6/9 = 0.666... The largest decimal is 0.75, corresponding to 3:4.

Question 11

Ramana spends 75% of his income. His income is increased by 25% and he increases his expenditure by 10%. By what percentage are his savings increased?

Accepted Answer

Assume income is 100. Expenditure is 75, savings 25. New income is 125. New expenditure is 75 * 1.10 = 82.5. New savings = 125 - 82.5 = 42.5. Percentage increase in savings = ((42.5 - 25) / 25) * 100 = 70%.

Question 12

A largest possible sphere is carved in a cube of side 14 cm. What is its volume in cm3?

Accepted Answer

The diameter of the largest sphere carved from a cube is equal to the cube's side. So, radius is 7 cm. Volume = (4/3)πr³ = (4/3) * (22/7) * 7³ = 1437.33 cm³.

Question 13

The respective ratio between numerical values of the curved surface area and the volume of a right circular cylinder is 2 ∶ 3. If the respective ratio between the radius and the height of the cylinder is 3 ∶ 7, what is the total surface area of the cylinder?

Accepted Answer

Given CSA/Volume = 2/3 and r/h = 3/7. Use formulas 2πrh / πr²h = 2/3 to find r=3. Then h=7. Calculate TSA = 2πr(r+h) = 2π(3)(3+7) = 60π cm².

Question 14

If 1234567y is divisible by 11, then what is the value of y?

Accepted Answer

For a number to be divisible by 11, the difference between the sum of digits at odd places and the sum of digits at even places must be 0 or a multiple of 11. (y+6+4+2) - (7+5+3+1) = 0. So, y+12 - 16 = 0, which gives y-4=0, hence y=4.

Question 15

O is the centre and the arc PQR subtends an angle of 240° at O. PQ is extended to A. Then ∠AQR is:

Accepted Answer

The reflex angle PQR at the center is 240°. The angle subtended by the arc at the circumference, ∠PQR, is half of this, so 120°. Since AQR is a straight line, ∠AQR = 180° - ∠PQR = 180° - 120° = 60°.

Question 16

Consider two concentric circles having radii 17 cm and 15 cm. What is the length (in cm)of the chord, of the bigger circle, which is a tangent to the smaller circle?

Accepted Answer

The radius of the larger circle (hypotenuse) is 17 cm, and the radius of the smaller circle (one leg) is 15 cm. Using Pythagoras theorem, the other leg is sqrt(17^2 - 15^2) = sqrt(289 - 225) = sqrt(64) = 8 cm. The chord length is twice this, so 2 * 8 = 16 cm.

Question 17

Study the given bar-graph and answer the question that follows.An electric vehicle company produces three different car models – A, B and C. The production of three different models over a period of four years (in lakhs) has been shown the bar-graph.The total production of model C in 2021 and 2022 is what percentage of the total production of model A in 2019 and 2020?

Accepted Answer

Calculate total production of C in 2021 and 2022 (110+110=220). Calculate total production of A in 2019 and 2020 (90+90=180). Percentage is (220/180)*100 = 122.22%.

Question 18

In ΔPQR, S and T are points on PQ and PR, respectively, such that ST ∥ QR and ST divides the ΔPQR into two parts of equal areas. Then the ratio of PS and QS is:

Accepted Answer

Since ΔPST ~ ΔPQR and Area(ΔPST) = 1/2 Area(ΔPQR), the ratio of sides PS/PQ = 1/√2. Thus, PS/QS = PS/(PQ-PS) = (PS/PQ)/(1-PS/PQ) = (1/√2)/(1-1/√2) = 1/(√2-1).

Question 19

A fraction‌35is decreased by‌25. The resulting fraction is then increased by 20%. What is the percentage decrease/increase in the value of the original fraction?

Accepted Answer

Original fraction is 3/5 = 0.6. Decreasing by 25% gives 0.6 * 0.75 = 0.45. Increasing by 20% gives 0.45 * 1.20 = 0.54. The change is 0.6 - 0.54 = 0.06. Percentage decrease is (0.06/0.6) * 100 = 10%.

Question 20

A man walking at the speed of 5 km/h covers a certain distance in 3 hours 45 minutes. If he covers the same distance by a cycle in 2 hours 10 minutes, then the speed of the cycle in km/h is:

Accepted Answer

First, calculate the distance covered: 5 km/h * (3 + 45/60) h = 5 * 3.75 = 18.75 km. Then, convert cycle time to hours: 2 + 10/60 = 2 + 1/6 = 13/6 hours. Finally, cycle speed = 18.75 / (13/6) = 18.75 * 6 / 13 = 112.5 / 13 = 8.65 km/h, which is 8 17/26.