SSC CHSL 2020 PYQs

Question 1

Quantitative AptitudeLength and breadth of rectangular field are in the ratio5:2. If the perimeter of the field is238m. Find the length of the field.

Accepted Answer

Let length be 5x and breadth be 2x. Perimeter = 2(5x + 2x) = 14x. Given perimeter is 238m, so 14x = 238, which means x = 17. Length = 5x = 5 * 17 = 85m.

Question 2

Quantitative AptitudeStudy the graph and answer the question.The above graph represents the salary, expenditure, tax and savings (in ₹) per month of the Persons A, B, C and D per month.The expenditure as a percentage of salary is the least for.

Accepted Answer

Calculate (Expenditure/Salary) * 100 for each person. Person B has the lowest ratio (10000/25000)*100 = 40%, making their expenditure percentage the least.

Question 3

Quantitative Aptitudecos‌x1+sin‌x+1+sin‌xcos‌xis equal to

Accepted Answer

Combine the fractions by finding a common denominator. This simplifies to (cos²x + (1+sin x)²) / (cos x (1+sin x)). Expand and use sin²x + cos²x = 1 to get (2 + 2sin x) / (cos x (1+sin x)). Factor out 2 from the numerator and cancel (1+sin x) to get 2/cos x, which is 2sec x.

Question 4

Quantitative AptitudeFind the value ofcos230−sin230sin215°+cos215°

Accepted Answer

Use the identity cos(2θ) = cos²θ - sin²θ and sin²θ + cos²θ = 1. The expression simplifies to cos(2*30°)/1 = cos(60°) = 1/2.

Question 5

In the given figure, BC is a chord and CD is a tangent through the point C. If∠AOC=118°, then find the∠ACD.

Accepted Answer

Angle subtended by an arc at the center is double the angle subtended at any point on the remaining part of the circle. So, ∠ABC = ∠AOC/2 = 118°/2 = 59°. By the alternate segment theorem, ∠ACD = ∠ABC = 59°.

Question 6

A man divided his journey into three parts of distances of18‌km,20‌kmand27‌km. He travelled the    distances at the speeds of6‌km∕h,5‌km∕hand9‌km∕h, respectively. What was his average speed during the entire journey ?

Accepted Answer

Calculate total distance (18+20+27=65 km) and total time (18/6 + 20/5 + 27/9 = 3+4+3 = 10 hours). Average speed is total distance divided by total time, so 65/10 = 6.5 km/h.

Question 7

The value of[0.9−{2.3−3.2−(7.1−5.4−3.5}]is

Accepted Answer

Follow BODMAS: first solve the innermost parenthesis (7.1 - 5.4 - 3.5 = -1.8). Then, 2.3 - 3.2 - (-1.8) = 2.3 - 3.2 + 1.8 = 0.9. Finally, 0.9 - 0.9 = 0.

Question 8

The factors of the expression2x2−5x−12are

Accepted Answer

Factorize 2x² - 5x - 12 by splitting the middle term. Find two numbers whose product is 2*(-12) = -24 and sum is -5. These are -8 and 3. So, 2x² - 8x + 3x - 12 = 2x(x-4) + 3(x-4) = (2x+3)(x-4).

Question 9

Rita's income is15%less than Richa's income. By what percent in Richa's income more than Rita's income?

Accepted Answer

If Rita's income is 15% less than Richa's, let Richa's income be 100. Rita's income is 85. The difference is 15. Percentage more = (15/85) * 100 = 17.64% or 17(11/17)%.

Question 10

The average age of 25 men is28‌yr, 5 new men of an average age of25‌yrjoined them. Find the average age of all the men together.

Accepted Answer

Calculate the total age of the initial 25 men (25*28 = 700) and the 5 new men (5*25 = 125). Sum these totals (700+125 = 825) and divide by the new total number of men (25+5 = 30) to get the average (825/30 = 27.5).

Question 11

The given graph represents the percentage distribution of the total expenditure of a company. Study the graph and answer the question that follows.What is the ratio of the total expenditure on 'Infrastructure' and 'Transport' to the total expenditure on 'Taxes' and 'Interest on Loans?

Accepted Answer

From the graph, Infrastructure (20%) + Transport (14%) = 34%. Taxes (10%) + Interest on Loans (16%) = 26%. The ratio is 34:26, which simplifies to 17:13.

Question 12

What is the distance between two parallel tangents of a circle of radius8‌cm?

Accepted Answer

The distance between two parallel tangents of a circle is equal to its diameter. Since the radius is 8 cm, the diameter is 2 * 8 = 16 cm.

Question 13

The area of a rectangle isa2−b2and its length isa+b, what will be its breadth?

Accepted Answer

The area of a rectangle is length × breadth. Given area = a²−b² and length = a+b. Since a²−b² = (a+b)(a−b), the breadth must be (a−b).

Question 14

Ifsec‌θ−tan‌θ=3, thencos‌θis equal to

Accepted Answer

Use the identity sec²θ - tan²θ = 1. Given secθ - tanθ = 3, find secθ + tanθ = 1/3. Solve these two equations simultaneously to get secθ = 5/3. Then cosθ = 1/secθ = 3/5.

Question 15

The least value of8cosec2θ+25sin2θis

Accepted Answer

Apply AM-GM inequality: For positive numbers a and b, (a+b)/2 ≥ √ab. Here, a=8cosec²θ and b=25sin²θ. So, 8cosec²θ+25sin²θ ≥ 2√(8cosec²θ * 25sin²θ) = 2√(200) = 2 * 10√2 = 20√2.

Question 16

In the given figure, O is the centre of the circle. Its two chords AB and CD intersect each other at the point P within the circle. IfAB=15‌cm,PB=9‌cm,CP=3‌cm, then find the length of PD.

Accepted Answer

Using the intersecting chords theorem, PA × PB = CP × PD. First, find PA = AB - PB = 15 - 9 = 6 cm. Then, 6 × 9 = 3 × PD, so PD = 54 / 3 = 18 cm.

Question 17

What is the radius of the circle whose area is equal to the sum of the areas of two circles whose radii are15‌cmand8‌cm?

Accepted Answer

The area of the new circle is πR² = π(15²) + π(8²). Simplifying, R² = 225 + 64 = 289. Thus, R = √289 = 17 cm.

Question 18

The radius of a circular cone is6‌cmand its height is7‌cm. Then, the volume of cone (incm3)is(Takeπ=227)

Accepted Answer

The volume of a cone is (1/3)πr²h. Substitute r=6 cm, h=7 cm, and π=22/7 to get (1/3) * (22/7) * 6² * 7 = 264 cm³.

Question 19

Observe the following bar-graph carefully and answer the following questions.The birth rate of Country C is approximately what percentage of the birth rate of Country E?

Accepted Answer

From the bar graph, Country C's birth rate is 12 and Country E's is 20. Calculate (12/20) * 100 = 60%.

Question 20

Richa travels from A to B at the speed of15‌km∕h, from B to C at20‌km∕hand from C to D at30‌km∕h. IfAB=BC=CD, then find the Richa's average speed.

Accepted Answer

Since distances are equal, use the harmonic mean formula for average speed: 3 / (1/15 + 1/20 + 1/30) = 3 / (4+3+2)/60 = 3 / (9/60) = 3 * 60 / 9 = 180 / 9 = 20 km/h.