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# Ratio and Proportion Questions for SSC CGL Set-3 PDF

Download SSC CGL Ratio and Proportion Questions with answers PDF based on previous papers very useful for SSC CGL exams. Very important Ration and Proportion Questions for SSC exams.

Question 1: The sum of the series (1 + 0.6 + 0.06 + 0.006 + 0.0006 + ….) is

a) 1$\frac{2}{3}$

b) 1$\frac{1}{3}$

c) 2$\frac{1}{3}$

d) 2$\frac{2}{3}$

Question 2: If the ratio of cost price and selling price of an article be as 10:11, the percentage of profit is

a) 8

b) 10

c) 11

d) 15

Question 3: A shopkeeper earns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of the cost price and the printed price of the book is

a) 45:56

b) 45:51

c) 47:56

d) 47:51

Question 4: Two natural numbers are in the ratio 3:5 and their product is 2160. The smaller of the numbers is

a) 36

b) 24

c) 18

d) 12

Question 5: $\frac{\sqrt{3+x} + \sqrt{3-x}}{\sqrt{3+x} – \sqrt{3-x}}$ = 2 then x is equal to

a) 5/12

b) 12/5

c) 5/7

d) 7/5

Question 6: If Rs. 1000 is divided between A and B in the ratio 3:2, then A will receive

a) Rs. 400

b) Rs. 500

c) Rs. 600

d) Rs. 800

Question 7: What must be added to each term of the ratio 7:11, so as to make it equal to 3:4 ?

a) 8

b) 7.5

c) 6.5

d) 5

Question 8: If the circumference of a circle is decreased by 50% then the percentage of decrease in its area is:

a) 25

b) 50

c) 60

d) 75

InstructionsDirections :The pie chart, given here, represents the number of valid votes obtained by four students who contested election for school leadership. The total number of valid votes polled was 720. Observe the chart and answer the questions based on it.

Number represented in pie-chart are in degrees.

Question 9: What was the minimum number of votes obtained by any candidate ?

a) 100

b) 110

c) 120

d) 130

Question 10: By how many votes did the winner defeat his nearest rival ?

a) 40

b) 45

c) 48

d) 50

Question 11: Two number are in the ratio 7:1 1. If 7 is added to each of the numbers, the ratio becomes 2:3. The smaller number is

a) 39

b) 49

c) 66

d) 77

Question 12: If an article is sold at 200% profit, then the ratio of its cost price to its selling price will be:

a) 1:2

b) 2:1

c) 1:3

d) 3:1

Question 13: The ratio of milk and water in mixtures of four containers are 5:3, 2:1, 3:2 and 7:4 respectively. In which container is the quantity of milk, relative to water, minimum?

a) First

b) Second

c) Third

d) Fourth

Question 14: Two numbers are in the ratio 1:3. If their sum is 240, then their difference is:

a) 120

b) 108

c) 100

d) 96

Question 15: The ratio of income and expenditure of a person is 11:10. If he saves IRS. 9,000 per annum. his monthly income is:

a) Rs. 8,000

b) Rs. 8,800

c) Rs. 8,500

d) Rs. 8,250

Given:
Summation of numbers (1 + 0.6 + 0.06….)
as we can see that the sequence 0.6, 0.06, 0.006 is making infinite g.p. with common ratio of 0.1
as we know summation of an infinite g.p. is $\frac{a}{1-r}$ (where a is first term and r is common ratio)
hence summation will be $\frac{0.6}{1-0.1}$ = $\frac{2}{3}$

Now the total sum will be 1+$\frac{2}{3}$ = 1$\frac{2}{3}$

Let the cost price be 10x and selling price be 11x

Percentage Profit = $\frac{11x – 10x}{10x}$ x 100 = 10

Given: Profit = 12%
Discount on printed price = 10%
Let’s say cost price is $x$ and printed price is $y$
hence sold price will be $x$ + $\frac{12x}{100}$ and $y$ – $\frac{10y}{100}$
Both should be equal:
hence $x$ + $\frac{12x}{100}$ = $y$ – $\frac{10y}{100}$
$\frac{x}{y}$ = $\frac{45}{56}$

Given:
Ratio of two numbers = 3:5
Hence we can say first number is $3x$ and second number is $5x$
Product of two numbers is = 2160
or $15x^{2}$ = 2160
or $x$ = 12
hence numbers will be 30 and 60

Let’s say $\sqrt{3+x}$ = a
and $\sqrt{3-x}$ = b
hence $\frac{a+b}{a-b}$ = 2
Now let’s say $\frac{a}{b}$ = $y$
According to ratio proportionate rule  $\frac{a+b}{a-b}$ =  $\frac{y+1}{y-1}$
After putting value and solving for $y$, its value will be 3
hence $\frac{a}{b}$ = 3
now putting a = $\sqrt{3+x}$ and $\sqrt{3-x}$ = b and solving for $x$
we will get $x$=$\frac{12}{5}$

Given: ratio of A and B is 3:2 and total money to be divided 1000
let’s say A received $3x$ and B received $2x$
hence  $3x$ +  $2x$ = 1000
or $x$ = 200

Given: Terms are in ratio 7:11
let’s say first term $7x$ and second term $11x$
adding $y$ to each term, it will be $7x+y$ and $11x+y$
and its ratio will be 3:4
hence $7x+y$ : $11x+y$ = 3:4
on solving above equation we get $5x$ = $y$
hence adding number should be a multiple of 5.

As we know circumference of a circle will be directly proportional to its radius $r_{1}$
hence when it got half its radius will also get half
now area of a circle is directly proportional to square of its radius
hence when its radius gets half its area gets $\frac{1}{4}$th of its value
let us say area was A
after decrement it will be $\frac{A}{4}$
Decrement is of $\frac{3A}{4}$ which is 75% of its original value.

Numbers of votes will be proportional to degree of angles in pie chart
hence minimum angle is representing the minimum distribution
so yasin will be having minimum number of votes which will be $\frac{60}{360}\times720=120$

As we know the number of votes will be directly proportional to the distribution
Shivaraman has the maximum no. of votes which will be $\frac{120}{360}\times720$=240
and secondly viswanath has number of votes $\frac{100}{360}\times720$=200
Hence difference will be 40

Let’s say numbers are $7x$ and $11x$
adding 7 to each of them
hence $\frac{7x+7}{11x+7}$ = $\frac{2}{3}$
or $x$ = 7
smaller digit will be 49

As we know cost price + profit = selling price
let’s say cost price is $x$
as profit is 200% on cost price it will be $2x$
hence selling price will be 3x and ratio of cost price to selling price will be 1:3

In first container quantity of milk relative to water is $\frac{5}{3} \times100$ = 166.65%
In second container quantity of milk relative to water is $\frac{2}{1} \times100$ = 200%
In third container quantity of milk relative to water is $\frac{2}{1} \times100$ = 150%
In fourth container quantity of milk relative to water is $\frac{7}{4} \times100$ = 175%
hence third container has least ratio

let’s say one number is $x$ and another is $3x$
summation will be $4x$ = 240
$x$ = 60
hence number will be 60 and 180
and difference will be 120.

let’s say income is $11x$ and expenditure is $10x$ hence saving will be $x$
so when saving is $x$, annual income is $11x$