Learn and practice the chapter "Ratio and Proportion" with these solved Aptitude Questions and Answers. Each question in the topic is accompanied by a clear and easy explanation, diagrams, formulae, shortcuts and tricks that help in understanding the concept.

Use of Ratio and Proportion Questions

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1. Which of the following two ratios is greater?

15

and

9

13

11

a.

15

13

b.

9

11

c. Both are same
d. Cannot determine

Answer: a.

15

13

Explanation:

It is easier to compare the fractions if they have common denominators.
Let's try to do that:
We have 13 and 11 in the denominator.
So, multiply first fraction up and down with 11 as shown

∴

15 x 11

=

165

------------------> 1^{st}

13 x 11

143

Multiply second fraction up and down with 13 as shown

∴

9 x 13

=

117

--------------------> 2^{nd}

11 x 13

143

Numerator of 1^{st} is greater (165 > 117); so 15:13 is greater than 9:11

Tip:
- If numerator of 1^{st} was smaller, when denominators were same, then 1^{st} fraction would have been smaller than 2^{nd}.

2. Find the 3^{rd} proportional to 9 and 72.

a. 8
b. 216
c. 576
d. 648

Answer: c. 576

Explanation:

In a:b:c, 3^{rd} proportional is c.
a:b:c can be written as a:b::b:c

a:b::b:c can be written as

a

=

b

=> b^{2} = ac

b

c

Here, a:b:c = 9:72:c
∴ 72 x 72 = 9 x c

∴ c =

72 x 72

= 576

9

3. Find the 4^{th} proportional in 7, 23 and 217?

a. 66
b. 506
c. 713
d. 961

Answer: c. 713

Explanation:

In a:b::c:d , 4^{th} proportional is d.

a:b::c:d can be written as

a

=

c

=> d =

c x b

b

d

a

Here, a:b::c:d = 7:23::217:d

∴ d =

23 x 217

= 713

7

4. Find the mean proportional between 9 and 81?

a. 21
b. 27
c. 35
d. 729

Answer: b. 27

Explanation:

In a:b:c, mean proportional = b
a:b:c can be written as a:b::b:c

a:b::b:c =>

a

=

b

=> b^{2} = ac => b = ac

b

c

Here, a = 9; c = 81 ∴ b =9 x 81= 27

5. Rajesh and Somesh were classmates. Their earnings now are in the ratio 5:6. The ratio of their expenses is 7:9. Somesh saves Rs 3,000 every month while Rajesh saves Rs 1000/- more than Somesh. Find the total earnings and expenses of each of them.

a. Rajesh - 25000, 21000; Somesh - 30000, 27000
b. Rajesh - 30000, 27000; Somesh - 36000, 32000
c. Rajesh - 36000, 32000; Somesh - 30000, 27000
d. None of the above

Answer: a. Rajesh - 25000, 21000; Somesh - 30000, 27000

Explanation:

Income ratio = Rajesh : Somesh = 5:6 =

5

;

6

Common factor helps in finding actual values easily
So, take 'A' as common factor.
Income of Rajesh = 5A; Income of Somesh = 6A

Expenses of Rajesh

=

Rajesh Income - Rajesh Saving

=

7

Expenses of Somesh

Somesh Income -Somesh Saving

9

Since Rajesh save, Rs 1000/- more than Somesh, Rajesh's savings = Rs 4000/-

∴

5A-4000

=

7

6A-3000

9

∴ 9(5A-4000) = 7(6A-3000)
∴ A = 5000
Income of Rajesh = 5A = 25000 ; Income of Somesh = 6A = 30000 Spending of Rajesh =25000 - 4000 = 21000
Spending of Somesh = 30000 - 3000 = 27000