SSC CGL 2024 PYQs

Question 1

How many years will it take for ₹8,400 to amount to ₹11,928 at a simple interest rate of 7% per annum?

Accepted Answer

Calculate simple interest (11928-8400 = 3528). Use SI = (P*R*T)/100 to find time T. T = (3528 * 100) / (8400 * 7) = 6 years.

Question 2

In triangles ABC and DEF, AB = FD and ∠A = ∠D. The two triangles are congruent by SAS criterion if:

Accepted Answer

For SAS congruence, two sides and the included angle must be equal. Given AB = FD and ∠A = ∠D, the included sides must be AC and DE respectively for congruence.

Question 3

The value of sin230 – sin240 + sin245 – sin255 – sin235 + sin245 – sin250 + sin260 is:

Accepted Answer

Use the identity sin(90-x) = cos(x) and sin^2(x) + cos^2(x) = 1. Pair terms like sin^2(30) and sin^2(60) (which is cos^2(30)) to cancel out, resulting in 0.

Question 4

The points P and S are on the same side of the line segment QR, such that∠PQR=90∘,∠SRQ=90∘andPQ=SR. Select the correct statement.

Accepted Answer

Given ∠PQR = ∠SRQ = 90°, PQ = SR, and QR is common. By SAS congruence (Side-Angle-Side), ∆PQR ≅ ∆SRQ. The angle is included between the sides.

Question 5

X, Y, and Z are three points on a plane with XY = 11 cm, YZ = 13 cm, and XZ = 24 cm. The number of circles that travel through points X, Y, and Z is:

Accepted Answer

For three points to form a circle, they must be non-collinear. Here, XY + YZ = 11 + 13 = 24 cm, which equals XZ. This means X, Y, and Z are collinear, so no circle can pass through them.

Question 6

Study the given bar-graph and answer the question that follows.The bar-graph shows the sales of books (in thousands) from six branches (B1, B2, B3, B4, B5 and B6) of a publishingcompany during two consecutive years 2000 and 2001.The total sales of branch B6 for both the years is what percentage of the total sales of branch B3 for both the years (correct up to two decimal places)?

Accepted Answer

Calculate total sales for B6 (70+80=150) and B3 (95+110=205). Then, divide B6 sales by B3 sales and multiply by 100: (150/205) * 100 = 73.17%.

Question 7

There are two pipes to fill a tank. Together, they can fill the tank in 15 minutes. If one pipe can fill the tank in one and a half times as fast as the other, the faster pipe alone can fill the tank in:

Accepted Answer

Let the slower pipe take 'x' minutes. The faster pipe takes 'x/1.5' = '2x/3' minutes. Their combined rate is 1/x + 3/2x = 1/15. Solving for x gives x=25 minutes for the faster pipe.

Question 8

Find the area of a square, one of whose diagonals is 4.8 m long.

Accepted Answer

The area of a square can be found using the formula (diagonal^2)/2. So, (4.8 * 4.8) / 2 = 23.04 / 2 = 11.52 m^2.

Question 9

Two pipes, A and B, can fill a tank in 10 minutes and 20 minutes, respectively. The pipe C can empty the tank in 30 minutes. All the three pipes are opened at a time in the beginning. However, pipe C is closed 2 minutes before the tank is filled. In what time, will the tank be full (in minutes)?

Accepted Answer

Calculate the combined filling rate of A and B, and the emptying rate of C. For the last 2 minutes, only A and B work. Calculate the remaining work and the time taken by all three pipes together.

Question 10

The value of cos229° + cos261° is :

Accepted Answer

Use the identity cos(90°-θ) = sin(θ). So, cos(61°) = cos(90°-29°) = sin(29°). The expression becomes cos²29° + sin²29°, which equals 1.

Question 11

The marked price of an article is 26% more than its cost price. If a discount of 32% is given, what will be the loss percentage?

Accepted Answer

Assume CP is 100. MP = 100 + 26% of 100 = 126. Selling Price = 126 - 32% of 126 = 126 - 40.32 = 85.68. Loss = 100 - 85.68 = 14.32. Loss percentage is 14.32%.

Question 12

The value of 15 ÷ 3 of 2 × 2 + 9 ÷ 18 of 2 × 4 – 4 ÷ 8 × 2 is:

Accepted Answer

Apply BODMAS: first 'of', then division/multiplication from left to right, then addition/subtraction. This yields 15 ÷ 6 × 2 + 9 ÷ 36 × 4 – 1. Simplifying gives 5 + 1 – 1 = 5.

Question 13

Places A and B are 20 km apart on the highway. A car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in one hour. If they travelled towards each other, they met in 12 minutes. What are the speeds (in km/h) of two cars?

Accepted Answer

Let speeds be x and y. Same direction: x - y = 20/1 = 20. Opposite direction: x + y = 20/(12/60) = 100. Solving these equations gives x=60, y=40.

Question 14

Find the value of‌sec35∘cosec55∘−‌cos25∘sin65∘

Accepted Answer

Use complementary angle identities: cosec(90-A) = sec A and sin(90-A) = cos A. So, cosec 55° = sec 35° and sin 65° = cos 25°. The expression simplifies to 1 - 0 = 1.

Question 15

Which of the following numbers is divisible by both 2 and 5?

Accepted Answer

A number divisible by both 2 and 5 must end in 0. Only 63840 ends in 0, satisfying both divisibility rules.

Question 16

A payment of ₹120 is made with ₹10, ₹5 and ₹2 coins. A total of 25 coins are used. Which of the following is the number of ₹10 coins used in the payment?

Accepted Answer

Let x, y, z be the number of ₹10, ₹5, ₹2 coins. We have 10x + 5y + 2z = 120 and x + y + z = 25. By checking options, if x=4, then 5y+2z=80 and y+z=21. Solving gives y=10, z=11. This satisfies both equations.

Question 17

An article is marked at ₹550. If it is sold at a discount of 40%, then the selling price becomes 10% more than its cost price. What is the cost price (in ₹)?

Accepted Answer

Selling Price (SP) = 550 * (1 - 0.40) = 330. SP is also 1.10 * Cost Price (CP). So, 1.10 * CP = 330, which means CP = 330 / 1.10 = 300.

Question 18

Simplify the following.‌sin3A−cos3AsinA−cosA, where A is an acute angle.

Accepted Answer

Use the identity a³-b³ = (a-b)(a²+ab+b²). Substitute sinA for 'a' and cosA for 'b'. Simplify using sin²A + cos²A = 1 to get 1 + sinA cosA.

Question 19

If, on a marked price, the difference between selling prices with a discount of 65% and with two successive discounts of 30% and 40% is ₹105, then the marked price (in ₹) is:

Accepted Answer

Calculate the single equivalent discount for 30% and 40% as 30+40-(30*40)/100 = 58%. The difference between 65% and 58% is 7%. If 7% of marked price is ₹105, then marked price is ₹105/0.07 = ₹1500.

Question 20

If 45º and 65º are the angles of a triangle, then find the exterior angle of the third angle (remaining angle).

Accepted Answer

The sum of two interior angles equals the exterior angle of the third angle. So, 45º + 65º = 110º.