SSC CHSL 2022 PYQs

Question 1

What value must be given to ‘*’ to make 6347*25 exactly divisible by 11?

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. Applying this rule, the value of '*' is 8.

Question 2

In a trip, Ram covers a distance of 200 km in 10 hours. First he started his journey by bike at a speed of 15 km/h, after that his bike broke down and he traveled the rest of the journey with his friend's car at 25 km/h. The ratio of distances covered by bike and car is ________.

Accepted Answer

Let bike distance be D1, time T1, and car distance D2, time T2. D1 + D2 = 200 km, T1 + T2 = 10 hours. Using D=ST, we get 15T1 + 25T2 = 200. Solving these equations yields T1=5h, T2=5h. So, D1=75km, D2=125km. Ratio D1:D2 = 75:125 = 3:5.

Question 3

Simplify the following: 50% of [6 – {15 – [6 + 8 ÷ (5 – 3)] + 2}]

Accepted Answer

Apply BODMAS rule: (5-3)=2, then 8÷2=4. Inside brackets: [6+4]=10. Then {15-10+2}=7. Finally, 50% of [6-7] = 50% of -1 = -0.5.

Question 4

A man can complete a work in 20 days, and a woman can complete the same work in 10 days. If they work on it together for 5 days, then how many days will the woman take to complete the rest of the work?

Accepted Answer

Man's 1-day work = 1/20, Woman's 1-day work = 1/10. Together, they do (1/20 + 1/10) = 3/20 work per day. In 5 days, they complete 5 * (3/20) = 3/4 work. Remaining work = 1 - 3/4 = 1/4. Woman completes 1/10 work per day, so she takes (1/4) / (1/10) = 10/4 = 2.5 days.

Question 5

The marked price of 42 items was equal to the cost price of 70 items. The selling price of 25 items was equal to the marked price of 21 items. Calculate the percentage profit or loss from the sale of each item.

Accepted Answer

Let MP, CP, SP be marked, cost, selling price per item. Given 42MP = 70CP, so MP = (70/42)CP = (5/3)CP. Also, 25SP = 21MP. Substitute MP: 25SP = 21(5/3)CP = 35CP. So SP = (35/25)CP = (7/5)CP. Profit = SP - CP = (7/5)CP - CP = (2/5)CP. Profit percentage = (2/5) * 100 = 40%.

Question 6

If the cost price of 70 articles is equal to the selling price of 40 articles, what will be the profit percentage?

Accepted Answer

Let CP of 1 article be 1. Then CP of 70 articles = 70. SP of 40 articles = 70. SP of 1 article = 70/40 = 1.75. Profit = 1.75 - 1 = 0.75. Profit % = (0.75/1)*100 = 75%.

Question 7

If x +‌1X= - 13, what is the value of x4+‌1X4?

Accepted Answer

Given x + 1/x = -13. Square both sides to find x² + 1/x² = (-13)² - 2 = 169 - 2 = 167. Square again to find x⁴ + 1/x⁴ = (167)² - 2 = 27889 - 2 = 27887.

Question 8

If‌x2y2‌+‌‌y2x2‌=‌7, A possible of‌x3y3‌+‌‌y3x3is :

Accepted Answer

Let a = x/y. Then a² + 1/a² = 7. We know (a + 1/a)² = a² + 1/a² + 2, so (a + 1/a)² = 7 + 2 = 9. Thus, a + 1/a = ±3. Now, a³ + 1/a³ = (a + 1/a)(a² + 1/a² - 1) = (±3)(7 - 1) = ±18. So, 18 is a possible value.

Question 9

If the average marks of three batches of 30, 50 and 70 students is 55, 70 and 70 respectively, then the average marks of all the students is:

Accepted Answer

Calculate the total marks for each batch (students * average) and sum them. Divide this total by the total number of students (30+50+70) to find the overall average.

Question 10

Suraj travels 124 km at a speed of 31 km/h by bus, 96 km at a speed of 16 km/h using a car, and another 105 km at 7 km/h by car. Find his average speed for the entire distance travelled.

Accepted Answer

Calculate total distance (124+96+105 = 325 km) and total time (124/31 + 96/16 + 105/7 = 4+6+15 = 25 hours). Average speed is total distance/total time = 325/25 = 13 km/h.

Question 11

Find the total surface area of a closed hemisphere whose radius is 3.5 cm. (Use π = 22/7)

Accepted Answer

The total surface area of a closed hemisphere is 3πr². Substitute r = 3.5 cm and π = 22/7: 3 * (22/7) * (3.5)² = 3 * (22/7) * 12.25 = 3 * 22 * 1.75 = 115.5 cm².

Question 12

The difference between a single discount of 20% and two successive discounts of 16% and 4% on a bill of Rs 50,000 is:

Accepted Answer

Calculate the single discount amount (20% of 50,000). Then, find the effective successive discount using the formula A+B - (AB/100) and apply it to 50,000. The difference between these two amounts is the answer.

Question 13

If P varies directly as Q, and P = 227 when Q = 232, find P when Q = 116.

Accepted Answer

Since P varies directly as Q, P/Q is constant. So, 227/232 = P/116. Solving for P gives P = (227 * 116) / 232 = 227 / 2 = 113.5.

Question 14

The given pie chart presents the monthly expenses on the various heads and the savings of Mr. X's family, study the pie chart and answer the question that follows.If the total income of Mr. X is Rs.1,20,000, then how much does he pay for transport?

Accepted Answer

From the pie chart, transport expense is 10% of total income. Calculate 10% of ₹1,20,000 to find the amount spent on transport.

Question 15

A family spends 8% of its monthly income on charity. In a particular month, the family spent ₹1,200 on charity. What is the income in that month?

Accepted Answer

If 8% of the income is ₹1,200, then 1% is ₹1,200/8 = ₹150. Therefore, 100% (total income) is ₹150 * 100 = ₹15,000.

Question 16

The following pie chart describes the number distribution of research scholars department wise in a university. The strength of scholars of which two given subjects exceeds the combined strength of the scholars from Physics and Mathematics?

Accepted Answer

Calculate the combined percentage for Physics and Mathematics. Then, sum the percentages for each option and compare. Zoology (18%) + Education (20%) = 38%, which is greater than Physics (15%) + Mathematics (20%) = 35%.

Question 17

Kamal purchases 80 articles for ₹11,180 and sells them at a loss equal to the selling price of 6 articles. What will be the selling price of 1 article?

Accepted Answer

Let SP of 1 article be x. Total CP = ₹11,180. Loss = 6x. Total SP = 80x. CP = SP + Loss, so 11180 = 80x + 6x = 86x. Thus, x = 11180/86 = ₹130.

Question 18

If (x+‌1x) = 7.5, what is the value of (x³+‌1x³)?

Accepted Answer

Use the identity (a+b)³ = a³+b³+3ab(a+b). Substitute a=x, b=1/x. So, (x+1/x)³ = x³+1/x³+3(x)(1/x)(x+1/x). This simplifies to (7.5)³ = x³+1/x³+3(7.5). Calculate 7.5³ = 421.875 and 3*7.5 = 22.5. Thus, x³+1/x³ = 421.875 - 22.5 = 399.375.

Question 19

After allowing 15% discount, a dealer wishes to sell a machine for ₹1,22,700. At what price must the machine be marked?(Consider up to two decimals)

Accepted Answer

Let the marked price be MP. Selling Price (SP) = MP - 15% of MP = 0.85 * MP. Given SP = ₹1,22,700. So, MP = 1,22,700 / 0.85 = ₹1,44,352.94.

Question 20

Which of the following options is divisible by 11?

Accepted Answer

Apply the divisibility rule for 11: sum of digits at odd places minus sum of digits at even places should be 0 or a multiple of 11. For 28171, (1+1+2) - (7+8) = 4 - 15 = -11, which is a multiple of 11.