SSC CHSL 2020 PYQs

Question 1

On selling a bike for ₹ 2500 a seller incurs a loss of20%. What price would have caused him to lose 30%?

Accepted Answer

First, find the cost price (CP) using the 20% loss: CP = 2500 / (1 - 0.20) = 2500 / 0.8 = ₹3125. Then, calculate the selling price for a 30% loss: SP = 3125 * (1 - 0.30) = 3125 * 0.7 = ₹2187.5.

Question 2

If2x+y=6andxy=4, then find the value of8x3+y3.

Accepted Answer

Use the identity (a+b)³ = a³+b³+3ab(a+b). Here, a=2x and b=y. Substitute the given values 2x+y=6 and xy=4 to find 8x³+y³ = (2x+y)³ - 3(2x)(y)(2x+y) = 6³ - 6(4)(6) = 216 - 144 = 72.

Question 3

If7129p465is divisible by 9 , then the value ofpis

Accepted Answer

For a number to be divisible by 9, the sum of its digits must be divisible by 9. Summing the digits 7+1+2+9+p+4+6+5 = 34+p. For 34+p to be divisible by 9, p must be 2 (since 34+2=36, which is divisible by 9).

Question 4

In the figure,'G' is the centre of the circle. Find the∠ACBwhen∠AGB=150°

Accepted Answer

The angle subtended by an arc at the center is double the angle subtended by the same arc at any point on the remaining part of the circle. So, ∠ACB = ∠AGB / 2 = 150° / 2 = 75°.

Question 5

M is the circumcentre ofΔ‌ABCwith circumradius15‌cm. LetBC=24‌cmand ML is perpendicular to BC. Then the length of ML is

Accepted Answer

M is the circumcenter, so MB = MC = circumradius = 15 cm. ML is perpendicular to BC, so L is the midpoint of BC. Thus, BL = BC/2 = 12 cm. In right-angled ΔMLB, ML² = MB² - BL² = 15² - 12² = 225 - 144 = 81. So, ML = 9 cm.

Question 6

Ifa−b=4anda3−b3=88, then find the value ofa2−b2.

Accepted Answer

Use a³−b³=(a−b)(a²+ab+b²) to find a²+ab+b². Then use (a−b)²=a²+b²−2ab to find ab. Finally, calculate a²+b² and then a²−b²=(a−b)(a+b).

Question 7

Study the graph and answer the question.The above graph represents the salary, expenditure, tax and savings (in ₹) details of the Persons A, B, C and D per month.The tax as a percentage of salary is highest in case of

Accepted Answer

Calculate (Tax/Salary)*100 for each person. For A: (1000/10000)*100 = 10%. For B: (1500/12000)*100 = 12.5%. For C: (2000/15000)*100 = 13.33%. For D: (1200/11000)*100 = 10.91%. C has the highest percentage.

Question 8

Ifaandbare two positive real numbers such that,a+b=20andab=4, then the value ofa3+b3is

Accepted Answer

Use the identity a³ + b³ = (a + b)(a² - ab + b²). Substitute a + b = 20 and ab = 4. Find a² + b² using (a + b)² = a² + b² + 2ab. Calculate to get 7760.

Question 9

The ratio of the areas of two squares is16:1. Find the ratio between their perimeters.

Accepted Answer

If the ratio of areas is A1:A2, then the ratio of sides is sqrt(A1):sqrt(A2). The ratio of perimeters is the same as the ratio of sides. So, sqrt(16):sqrt(1) = 4:1.

Question 10

InΔ‌XYZ,Land M are the middle points of the sides XY and XZ, respectively. R is a point on the segment LM, such thatLR:RM=1:2. IfLR=3‌cm, then YZ is equal to

Accepted Answer

Given LR = 3 cm and LR:RM = 1:2, so RM = 6 cm. Thus, LM = LR + RM = 9 cm. By the Midpoint Theorem, LM = 1/2 YZ. Therefore, YZ = 2 * LM = 2 * 9 = 18 cm.

Question 11

Ifx+y+z=10,x3+y3+z3=75andxyz=15, then find the value ofx2+y2+z2−xy−yz−zx

Accepted Answer

Use the identity x³+y³+z³-3xyz = (x+y+z)(x²+y²+z²-xy-yz-zx). Substitute the given values: 75 - 3(15) = 10 * (required expression). Simplify to find the answer.

Question 12

If the three sides of a triangle are11‌cm,12‌cmand13‌cm, then what is the area of the given triangle (incm2)?

Accepted Answer

Calculate the semi-perimeter (s) as (11+12+13)/2 = 18. Apply Heron's formula: Area = √[s(s-a)(s-b)(s-c)] = √[18(18-11)(18-12)(18-13)] = √[18*7*6*5] = √[3780] = 6√105.

Question 13

The given graph represents the rainfall (incm) in a city, over a period of six years. Study the graph and answer the question that follows.In which two consecutive years was the difference of the rain fall minimum?

Accepted Answer

Calculate the difference in rainfall for each consecutive year pair. The minimum difference is between 2005 (80 cm) and 2006 (75 cm), which is 5 cm.

Question 14

The diagonal of rectangle is15cm2and length is12cm2. Find the area of the rectangle.

Accepted Answer

Using Pythagoras theorem, breadth = sqrt(15^2 - 12^2) = sqrt(225 - 144) = sqrt(81) = 9 cm. Area = length * breadth = 12 * 9 = 108 cm^2.

Question 15

Mohan offers to sell his articles at a discount of20%, but he marks his articles by increasing the price of each by35%.What percentage would his gain be?

Accepted Answer

Assume CP is 100. Marked Price (MP) is 100 + 35% of 100 = 135. Selling Price (SP) is 135 - 20% of 135 = 135 - 27 = 108. Gain is SP - CP = 108 - 100 = 8. Percentage gain is (8/100)*100 = 8%.

Question 16

A person deposits ₹ 8000 in a bank which pays8%p.a. simple interest. The amount after8‌yrwill be

Accepted Answer

Calculate simple interest using P*R*T/100. Add the interest to the principal amount to find the total amount after 8 years. Interest = 8000*8*8/100 = 5120. Amount = 8000 + 5120 = 13120.

Question 17

InΔ‌PQR, the side QR is extended to S such that,RS=PR. If∠QPS=110°and∠PRQ=70°, then the value of∠PQRis

Accepted Answer

Since PR = RS, triangle PRS is isosceles. ∠SPR = ∠PSR. Using exterior angle property for ΔPQR, ∠PRS = ∠PQR + ∠QPR. Solve for ∠PQR.

Question 18

In the given bar graph, the white bar shows the income and the black bar shows the expenditure of a company. Study the graph and answer the question that follows.The income in 2001 was equal to the expenditure in the year

Accepted Answer

From the graph, income in 2001 (white bar) is 40 units. Locate the black bar (expenditure) that is also 40 units. This corresponds to the year 2004.

Question 19

Find the value oftan‌60°−tan‌15°1+tan‌60°‌tan‌15°

Accepted Answer

The given expression matches the tan(A-B) identity: tan(A-B) = (tanA - tanB) / (1 + tanA tanB). Here, A=60° and B=15°. So, the expression simplifies to tan(60°-15°) = tan(45°) = 1.

Question 20

Ifsin‌x=1237, then what is the value oftan‌x?

Accepted Answer

Given sin x = 12/37 (opposite/hypotenuse). Using Pythagoras theorem, adjacent side = sqrt(37^2 - 12^2) = sqrt(1369 - 144) = sqrt(1225) = 35. So, tan x = opposite/adjacent = 12/35.