SSC GD 2021 PYQs

Question 1

A single discount equivalent to three successive discounts i.e. 7%, 12% and 5% is:

Accepted Answer

Calculate the effective discount for 7% and 12% first using A+B-(AB/100). Then, apply this result with the 5% discount using the same formula to find the single equivalent discount.

Question 2

Simplify the following expression.	ext"$\;{\;{3}/{4}\;of\;	ext\;""\;"\;1{3}/{5}−1\;×\;5\;+\;2}/{24−6\;+\;2} ÷ 4$

Accepted Answer

Using BODMAS: Numerator = 3/4 of 8/5 - 5 + 2 = 6/5 - 3 = -9/5. Denominator = 24 - 6 + 2 = 20. Result = (-9/5) / 20 ÷ 4 = -9/400.

Question 3

Two numbers are 8% and 28%, respectively, more than a third number. What is the ratio between the two numbers?

Accepted Answer

Assume the third number is 100. The first number is 108 (100+8%) and the second is 128 (100+28%). The ratio is 108:128, which simplifies to 27:32.

Question 4

An article was sold at‌118times of its cost price. The profit per cent is:

Accepted Answer

If SP = (11/8)CP, then Profit = SP - CP = (11/8)CP - CP = (3/8)CP. Profit percentage is (Profit/CP) * 100 = (3/8) * 100 = 37.5%.

Question 5

Find the ratio of the diagonal of a square of side 15 cm, to its side.

Accepted Answer

The diagonal of a square with side 'a' is a√2. The ratio of diagonal to side is a√2 : a, which simplifies to √2 : 1.

Question 6

Radha saves 28% of her income. If her expenditure increases by 25% and savings increase by 30%, then by what percentage will her income increase?

Accepted Answer

Assume income is 100. Savings = 28, Expenditure = 72. New expenditure = 72 * 1.25 = 90. New savings = 28 * 1.30 = 36.4. New income = 90 + 36.4 = 126.4. Percentage increase = (126.4 - 100)/100 * 100 = 26.4%.

Question 7

A batsman scored 124 runs, which included 6 boundaries and 10 sixes. What percentage of his total score did he make by running between the wickets?

Accepted Answer

Runs from boundaries (6*4) = 24. Runs from sixes (10*6) = 60. Total runs from boundaries/sixes = 84. Runs by running = 124 - 84 = 40. Percentage = (40/124) * 100 = 32.25% or 32 8/31%.

Question 8

Two trains start from places A and B. respectively, and travel towards each other at the speeds of 60 km/h and 50 km/h. respectively. By the time they meet, the faster train has travelled 110 km more than the slower train. What is the distance between A and B?

Accepted Answer

Let time be T. Faster train travels 60T, slower 50T. Difference is 10T = 110 km, so T = 11 hours. Total distance = (60+50) * 11 = 110 * 11 = 1210 km.

Question 9

By selling 18 oranges for ₹151.20, a man loses 20%. How many oranges should he sell for ₹819 to earn a profit of 30%?

Accepted Answer

First, find the cost price of one orange. Then, calculate the selling price per orange for a 30% profit. Finally, divide the target amount by this new selling price to find the number of oranges.

Question 10

A man bought two mobiles phones for ₹50,000. He sold one of them at a profit of 15% and the other at a loss of 20%. If the selling price of each mobile is the same, what is the approximate cost price (to the nearest rupee) of the mobile that was sold at a loss?

Accepted Answer

Let CP1 and CP2 be the cost prices. SP1 = 1.15 * CP1 and SP2 = 0.80 * CP2. Since SP1 = SP2, 1.15 * CP1 = 0.80 * CP2. Also, CP1 + CP2 = 50000. Solve these equations to find CP2 ≈ ₹29,487.

Question 11

The value of[6+3 of\;	ext""‌7−5]÷2 of\;	ext""‌11is:

Accepted Answer

Apply BODMAS: first 'of' (multiplication), then addition/subtraction inside brackets, finally division. [6 + 21 - 5] ÷ 22 = [27 - 5] ÷ 22 = 22 ÷ 22 = 1.

Question 12

The amount obtained by investing a certain sum at r% p.a. for 3 years at simple interest is equal to the simple interest on the same sum at the same rate for 19 years. What is the value of r ?

Accepted Answer

Let the sum be P. Amount = P + (P*r*3)/100. Simple Interest = (P*r*19)/100. Equating them: P + 3Pr/100 = 19Pr/100. This simplifies to 1 = 16r/100, so r = 100/16 = 6.25.

Question 13

A man incurred 8% loss by selling a TV for ₹18,400. At what price should the TV be sold to earn 5% profit?

Accepted Answer

First, find the cost price (CP). If ₹18,400 is 92% of CP (100%-8% loss), then CP = 18400 / 0.92 = ₹20,000. To earn 5% profit, selling price (SP) = 20000 * 1.05 = ₹21,000.

Question 14

If the difference between two numbers is 42 and their LCM and HCF are 1729 and 7, respectively, what is the sum of those two numbers?

Accepted Answer

Let the numbers be 7a and 7b. Their product is LCM × HCF = 1729 × 7. So, 49ab = 1729 × 7, which gives ab = 247. The difference is 7a - 7b = 42, so a - b = 6. Using (a+b)^2 = (a-b)^2 + 4ab, we get (a+b)^2 = 6^2 + 4(247) = 36 + 988 = 1024. Thus, a+b = 32. The sum of numbers is 7(a+b) = 7 × 32 = 224.

Question 15

A sum at a certain rate of simple interest becomes ₹37,200 after 3 years and ₹42,000 after 5 years. Find the simple interest (in ₹ ) on the same sum at 6% per annum for 8 years.

Accepted Answer

The interest for 2 years (5-3) is ₹4800 (42000-37200). Annual interest is ₹2400. Principal is ₹37200 - (3 * 2400) = ₹30000. Required SI = (30000 * 6 * 8) / 100 = ₹14400.

Question 16

A trader buys two articles A and B for ₹600. He sells A at 20% profit and B at 10% loss. If he gains 8% in the whole transaction, then the cost price (in ₹) of article A is:

Accepted Answer

Let CP of A be x. CP of B is (600-x). Total profit is 8% of 600 = 48. Profit on A is 0.2x, loss on B is 0.1(600-x). Set up equation: 0.2x - 0.1(600-x) = 48. Solve for x.

Question 17

There are 45 persons (only male and female) in a group. The ratio of the number of males and females is 5 : 4. If the average weight of males is 79.4 kg and that of females is 64.5 kg, then what will be the average weight (in kg) of all the individuals in the group (corrected to one decimal place)?

Accepted Answer

Calculate the number of males (25) and females (20) from the ratio. Then, use the weighted average formula: (25*79.4 + 20*64.5) / 45. This yields 72.77, which rounds to 72.8 kg.

Question 18

A sum of Rs. 10500 amounts to Rs. 12705 in 2 years at x % p.a., when the interest is compounded annually. The same sum will amount (in Rs.) to what at 2 x % p.a. in 1‌12years, when interest compounded half yearly?

Accepted Answer

First, calculate 'x' using the compound interest formula for the initial scenario. Then, apply this 'x' to find the amount with 2x% interest compounded half-yearly for 1.5 years. The final amount is Rs. 13975.50.

Question 19

The greatest number that will divide 398, 437 and 5425 leaving 7, 12 and 2 as remainders, respectively, is:

Accepted Answer

Subtract the remainders from the respective numbers: 398-7=391, 437-12=425, 5425-2=5423. The greatest number is the HCF of 391, 425, and 5423, which is 17.

Question 20

The sides of a triangular park are 96 m. 110 m and 146 m. its area is equal to the area of a field in the shape of a rhombus, the one of whose diagonals is 60 m. The length(in m) of its other diagonal is:

Accepted Answer

First, calculate the area of the triangular park using Heron's formula. Then, equate this area to the area of the rhombus (1/2 * d1 * d2) and solve for the unknown diagonal.