SSC CHSL 2022 PYQs

Question 1

Find the radius of the circle x2+ y2- 4x + 6y = 12.

Accepted Answer

Rewrite the equation as (x-2)^2 + (y+3)^2 = 12 + 4 + 9 = 25. Comparing with (x-h)^2 + (y-k)^2 = r^2, the radius r is sqrt(25) = 5 cm.

Question 2

40% of Ranita’s income is equal to 56% of Bhaskar’s income. If Ranita’s income was ₹800 more than what it is and Bhaskar’s income was ₹2,000 more than what it is, then the ratio of the incomes of Ranita and Bhaskar would have been 4 ∶ 3. What is the actual combined income of Ranita and Bhaskar?

Accepted Answer

Let Ranita's income be R and Bhaskar's be B. From the first condition, 0.40R = 0.56B, so R = 1.4B. From the second condition, (R+800)/(B+2000) = 4/3. Substitute R=1.4B into the second equation to find B, then R, and finally R+B.

Question 3

P, Q and R are batsmen. The ratio of the runs scored by them in a certain match was P ∶ Q = 16 ∶ 17 and Q ∶ R = 15 ∶ 16. At the end of the match, they scored a total of 956 runs. The number of runs scored by R is (nearest to an integer):

Accepted Answer

Combine ratios P:Q = 16:17 and Q:R = 15:16 to get P:Q:R = 240:255:272. Total parts = 767. R's runs = (272/767) * 956 ≈ 339.

Question 4

Bhanu spends 20% of his monthly salary on rent, 10% on stationery, 14% on transport, 18% on electricity, and the balance of ₹1,520 on remaining items. What is the monthly salary of Bhanu?

Accepted Answer

Total known expenses are 20+10+14+18 = 62%. The remaining 100-62 = 38% of salary is ₹1,520. So, total salary is (1520/38)*100 = ₹4,000.

Question 5

Using 2cosA cosB = cos(A + B) + cos(A – B), find the value of cos75°cos15°.

Accepted Answer

Given 2cosA cosB = cos(A + B) + cos(A – B). So, cosA cosB = 1/2 [cos(A + B) + cos(A – B)]. Substitute A=75°, B=15° to get 1/2 [cos(90°) + cos(60°)] = 1/2 [0 + 1/2] = 1/4.

Question 6

Study the given graph carefully and answer the question that follows.Production of food grains by a state over the years (1000 tonnes)What was the percentage drop in the production of food grains from 2018 to 2019 (consider up to two decimals)?

Accepted Answer

Production in 2018 was 7000 tonnes and in 2019 was 6500 tonnes. Percentage drop = ((7000-6500)/7000) * 100 = (500/7000) * 100 = 7.14%.

Question 7

16 men can paint 15 walls in 45 days. In how many days can 20 men paint 20 walls?

Accepted Answer

Use the formula M1*D1/W1 = M2*D2/W2. Substitute the given values: 16*45/15 = 20*D2/20. Simplify to find D2 = 48 days.

Question 8

Find the greatest among the following options.

Accepted Answer

Convert all options to decimals: 0.62, 2/3 ≈ 0.666..., 0.57, 4/5 = 0.8. Comparing these values, 0.8 is the greatest.

Question 9

The value of tan 48°. tan 23°. tan 42°. tan 67° is

Accepted Answer

Use the identity tan(90°-θ) = cot θ. Pair tan 48° with tan 42° (cot 48°) and tan 23° with tan 67° (cot 23°). Since tan θ * cot θ = 1, the product simplifies to 1*1 = 1.

Question 10

Calculate the area of the quadrilateral formed with the vertices (-3, 2), (5, 4),(7, -6) and (-5, -4).

Accepted Answer

Use the shoelace formula: 1/2 |(x1y2 + x2y3 + x3y4 + x4y1) - (y1x2 + y2x3 + y3x4 + y4x1)|. Substitute the coordinates and calculate to get 80 square units.

Question 11

Study the given table and answer the question that follows.The table shows quanity of various food items used by a restaurant during four months of a year (in kg).Food ItemJuneJulyAugustSeptemberRice180200240300Wheat420400380350Sugar200210230240Pulses250310320280Vegetables300320390370The quantity of wheat used in the month of July is what percentage of the total quantity of food items used in June ?

Accepted Answer

Total food in June = 180+420+200+250+300 = 1350 kg. Wheat in July = 400 kg. Percentage = (400/1350) * 100 = 4000/135 = 29.629...% which is 29 17/27%.

Question 12

The distance between stations A and B is 778 kilometres. A train travels from station A to station B at a uniform speed of 84 km/h and then returns to station A at a uniform speed of 56 km/h. What is the train's average speed (in km/h) throughout the journey?

Accepted Answer

Average speed for equal distances is 2ab/(a+b). Substitute a=84 and b=56: 2*84*56 / (84+56) = 9408 / 140 = 67.2 km/h.

Question 13

Two grandparents, two parents, and three grandchildren make up a family. The average present age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the present age of the family (in years)?

Accepted Answer

Calculate total age for each group: Grandparents (2*67=134), Parents (2*35=70), Grandchildren (3*6=18). Sum these totals (134+70+18=222) and divide by total family members (2+2+3=7) to get 222/7 = 31.71 or 31 5/7.

Question 14

The pie chart shows the percentage-wise break up of students in terms of specialisation in Engineering.Total number of students = 8000What is the ratio of the total number of students having either Networking or Graphics as their specialisations to the number of students having C programming as their specialisation?

Accepted Answer

Networking + Graphics = 19% + 12% = 31%. C Programming = 17%. The ratio is 31:17. The total number of students (8000) is not needed for this ratio calculation.

Question 15

Ifx4+(‌1x4)=322, then what is the value ofx3−(‌1x3)?

Accepted Answer

From x⁴ + 1/x⁴ = 322, find x² + 1/x² = 18, then x - 1/x = 4. Finally, use the identity a³ - b³ = (a - b)(a² + ab + b²) to get x³ - 1/x³ = (x - 1/x)(x² + 1/x² + 1) = 4(18 + 1) = 4 × 19 = 76.

Question 16

If x2= b - ax and x3(x3+ c) = d, then which of the following can be the values of c and d?

Accepted Answer

From x² = b - ax, we get x² + ax = b. Cube both sides: (x² + ax)³ = b³. Expand using (A+B)³ formula to find x⁶ + a³x³ + 3ax(x² + ax) = b³. Substitute x² + ax = b to get x⁶ + a³x³ + 3abx³ = b³. Rearrange to x³(x³ + a³ + 3ab) = b³. Comparing with x³(x³ + c) = d, we find c = a³ + 3ab and d = b³.

Question 17

The cost price of an article is Rs.6,450. If it sold at a profit 16%, how much would be its selling price?

Accepted Answer

Selling Price = Cost Price × (1 + Profit Percentage). Calculate 16% of 6450 (which is 1032) and add it to 6450 to get 7482.

Question 18

If P : Q = 10 : 11 and Q : R = 11 : 12, then P + Q : Q + R : R + P is:

Accepted Answer

Given P:Q = 10:11 and Q:R = 11:12. Since Q is common and has the same value (11), we can directly write P:Q:R = 10:11:12. Then calculate P+Q, Q+R, R+P.

Question 19

Study the given pie-chart and answer the question that follows.The pie-chart shows the data for A, B, O, AB blood groups of 240 donors.The ratio of the donors of blood group ‘O’ to the average of the donors of groups ‘A’ and ‘AB’ is:

Accepted Answer

Calculate the number of donors for O, A, and AB groups using their percentages. Then find the average of A and AB donors. Finally, determine the ratio of O donors to this average.

Question 20

A shopkeeper normally makes a profit of 20% in a certain transaction; he weights 900 g instead of 1 kg, due to an issue with the weighing machine. If he charges 10% less than what he normally charges, what is his actual profit or loss percentage?

Accepted Answer

Assume CP of 1kg is Rs 100. Shopkeeper sells 900g for Rs 108 (120% of 90% of 100). Actual CP for 900g is Rs 90. Profit = (108-90)/90 * 100 = 20%.