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

The questions and examples given in this section will be useful to all the freshers, college students and engineering students preparing for placement tests or any competitive exam like MBA, CAT, MAT, SNAP, MHCET, XAT, NMAT, GATE, Bank exams - IBPS, SBI, RBI, RRB, SSB, SSC, UPSC etc.

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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}.

Video : Ratio and Proportion in Hindi - Simple Aptitude tricks for freshers

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