SSC GD 2023 PYQs

Question 1

Find the fourth proportional to the numbers 36, 48 and 90.

Accepted Answer

For numbers a, b, c, the fourth proportional d is found by a/b = c/d. So, 36/48 = 90/d. Solving for d gives d = (48 * 90) / 36 = 120.

Question 2

Find the sum of the digits of the smallest 6-digit number divisible by 18, 24 and 25.

Accepted Answer

Find the LCM of 18, 24, 25, which is 3600. The smallest 6-digit number is 100000. Divide 100000 by 3600, remainder is 2800. Add (3600-2800) = 800 to 100000 to get 100800. Sum of digits is 1+0+0+8+0+0 = 9.

Question 3

Sohan borrowed money at the rate of 20% per annum on compound interest, interest was compounding annually and he paid it in three equal instalments, each instalment was to be paid at the end of every year. If each instalment was for ₹1,250, then the money borrowed by Sohan was (nearest integral value):

Accepted Answer

Use the present value of annuity formula for compound interest. P = x / (1+r) + x / (1+r)^2 + x / (1+r)^3. Substitute x=1250 and r=0.20 to find P ≈ ₹2633.

Question 4

Arun and Aditya can complete a work separately in 8 days and 12 days, respectively. After 2 days of working alone, Aditya leaves the work, In how many days Arun will complete the remaining work?

Accepted Answer

Aditya's 2-day work is 2/12 = 1/6. Remaining work is 1 - 1/6 = 5/6. Arun's daily work is 1/8. Time for Arun to complete remaining work = (5/6) / (1/8) = 40/6 = 6 2/3 days.

Question 5

Mohan is selling a table at Rs. 2,832. If his profit is 18%, then what is the cost price of the table?

Accepted Answer

Let CP be x. SP = CP + Profit. So, 2832 = x + 0.18x = 1.18x. Therefore, x = 2832 / 1.18 = 2400. The cost price is Rs. 2400.

Question 6

A cylindrical tank has a capacity of 5632 m3. If the diameter of its base is 16 m, find its depth.

Accepted Answer

The volume of a cylinder is πr²h. Given volume = 5632 m³ and diameter = 16 m, so radius r = 8 m. Substitute values: 5632 = (22/7) * 8² * h. Solving for h gives 28 m.

Question 7

Evaluate the following expression.[‌−47÷‌112]÷[−‌45×{.(−2)−(−‌27)]

Accepted Answer

Simplify the expression using BODMAS. First, calculate inside the brackets: [(-4/7) ÷ (1/12)] = -48/7. Then, [-4/5 × (-2 + 2/7)] = [-4/5 × (-12/7)] = 48/35. Finally, divide: (-48/7) ÷ (48/35) = -5.

Question 8

In a proportion. the product of the 1stand 4thterm is 70 and that of 2ndand 3rdterm is 3.5x The value of x is:

Accepted Answer

In a proportion, the product of the extremes (1st and 4th terms) equals the product of the means (2nd and 3rd terms). Set 70 = 3.5x and solve for x.

Question 9

Out of 10 persons, 9 persons spent ₹15 each on their breakfast. The tenth person spent ₹9 more than the average expenditure of all of them. The total amount spent by all of them is:

Accepted Answer

Let the average expenditure be 'x'. Total expenditure = 10x. 9 people spent 9*15 = 135. The 10th person spent x+9. So, 10x = 135 + x + 9. Solving for x, 9x = 144, so x = 16. Total expenditure = 10 * 16 = 160.

Question 10

In a mixture of 60 litres, the ratio of milk and water is 2 ∶ 3. What amount of water must be added to make the ratio of milk and water 1 ∶ 2?

Accepted Answer

Initially, milk is 24L and water is 36L. To achieve a 1:2 ratio with 24L milk, water needs to be 48L. So, 48L - 36L = 12L water must be added.

Question 11

The value of 1 ÷ 2 + 3 - 5 ×‌13of 15 - {75 ÷ (28 - 3)} is:

Accepted Answer

Apply BODMAS: first solve brackets, then 'of', division, multiplication, addition, and finally subtraction. The calculation simplifies to 1/2 + 3 - 25 - 3, resulting in -49/2.

Question 12

The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Rs. 80. The sum (in Rs.) is:

Accepted Answer

Use the formula: Difference = P * (R/100)^2. Substitute the given values: 80 = P * (4/100)^2. Solve for P to get 50,000.

Question 13

Rs. 11,500 is borrowed at compound interest at the rate of 5% per annum, compounding annually. What will be the amount to be paid after 2 years?

Accepted Answer

Use the compound interest formula A = P(1 + R/100)^T. Substitute P=11500, R=5, T=2. Calculate A = 11500 * (1.05)^2 = 11500 * 1.1025 = 12678.75.

Question 14

Ravi can decorate a wall in 6 hours, while Ankita can decorate the same wall in 10 hours. In how many hours will they decorate the wall working simultaneously?

Accepted Answer

Ravi's rate is 1/6 wall/hour, Ankita's is 1/10 wall/hour. Combined rate is 1/6 + 1/10 = 8/30 = 4/15 wall/hour. Time taken is 1 / (4/15) = 15/4 = 3.75 hours.

Question 15

In how much time (in years) would ₹80,000 amount to ₹1,17,128 at 10% per annum rate of interest, compounded yearly?

Accepted Answer

Use the compound interest formula A = P(1 + R/100)^T. Substitute the given values: 117128 = 80000(1 + 10/100)^T. Simplify to (1.1)^T = 1.4641. Recognize that 1.4641 is (1.1)^4, so T = 4 years.

Question 16

A shopkeeper sells goods at a profit of 12% and uses a weight that is 15% less than the original weight. Find his total percentage gain. (Correct to 2 decimal places)

Accepted Answer

Assume CP of 1000g is Rs 1000. Shopkeeper sells 850g (15% less) for Rs 1120 (12% profit). Total profit is (1120-850)/850 * 100 = 31.76%.

Question 17

The volumes of two cones are in the ratio of 3 ∶ 2 and their radii are in the ratio 3 ∶ 4. The ratio of their heights is:

Accepted Answer

The volume of a cone is (1/3)πr²h. Set up the ratio of volumes V1/V2 = (r1²/r2²) * (h1/h2). Substitute given ratios (3/2) = (3²/4²) * (h1/h2) and solve for h1/h2.

Question 18

A and B together can do a piece of the work in 50 hours, B and C together can do the same work in 75 hours and A and C together can do the same in 25 hours. Find the time in which A, B, and C together will complete the task.

Accepted Answer

Calculate individual work rates. Sum (A+B), (B+C), (A+C) rates to get 2(A+B+C)'s rate. Divide total work (LCM of 50, 75, 25 = 150) by (A+B+C)'s rate to find the time.

Question 19

Arun bought a laptop from Sanchit for Rs. 1,12,500. Sanchit earned a profit of 25% on the laptop. Raman sold the laptop to Sanchit at a gain of 20%. How much did Raman pay to buy the laptop?

Accepted Answer

Sanchit's selling price (Arun's cost) is Rs. 1,12,500. Sanchit's profit was 25%, so Sanchit's cost was 112500 / 1.25 = Rs. 90,000. Raman sold to Sanchit at 20% profit, so Raman's cost was 90000 / 1.20 = Rs. 75,000.

Question 20

A vegetable vendor does his sales using a weight which is 12% less than the actual weight and earns a profit of 32% on the cost price. Find the total profit percentage?

Accepted Answer

Assume actual weight is 100 units. Vendor sells 88 units but charges for 100. This gives a profit of (100-88)/88 = 12/88 = 13.63%. Combined with 32% profit, total profit is (1.1363 * 1.32 - 1) * 100 = 50%.