## Quantitative Aptitude Questions – Ratio and Proportion

**1.**

**Find the fourth proportional to the numbers 8,12 and 16**

**Explanation:**The fourth proportion of a,b and c is

bc
a

Therefore, fourth proportional of 8,12 and 16 =

12 x 16
8

= 24**2.**

**What is the third proportional to 18, 12**

**?**

**Explnation:**Third proportion of a and b is

b

^{2}a
Third proportion of 18 and 12 =

12

= 8^{2}18**3.**

**What is the mean proportional between 16 and 25 ?**

**Explnation:**The mean proportional of a and b is √ a x b

∴ mean proportion of 16 and 25 is =
√ 16 x 25
=
√ 400
= 20

**4**.

**If A:B = 3:1 and B:C = 2:3 . What is the value of A:B:C?**

**Explnation:**In the given 2 ratios, the common term is B. To write the two ratios into a single ratio, the values of the common term must be equal.

A : B : C A
: B : C

3 : 1
x 2 6 : 2

2: 3

__2 : 3__
6 : 2 : 3

**5.**

**If A:B=2:5 , B:C = 5:4 and C:D = 6:1. Then what is the value of A : D ?**

**Explanation:**

A
B

x
B
C

x
C
D

=
A
D

∴ A:D =

2
5

x
5
4

x
6
1

=
3
1

= 3:1**6.**Rs 3798 is divided into parts in the ratio of 5:4. What is the value of the 1

^{st}part?

**Explanation:**: Divided in the ratio= 5:4

Sum of the parts= 5+4= 9

1

^{st}part = Rs 3798 = $\frac{5}{9}$ = Rs 2110**7.**

**A sum of money is divided between A and B in the ratio of 11:3 . The difference between their shares is Rs 6400. Find the total amount?**

**Explanation:**: Let A and B got 11x and 3x .

The difference
between their shares 11x – 3x = 8x =6400 =>x = 800

Total amount= Sum of the shares = 11x + 3x

=> 14x = 14 x 800 =Rs 11200

=> 14x = 14 x 800 =Rs 11200

**8.**The sum of the two numbers is 72. Which of the following cannot be the ratio of those two numbers ?

a)8:1 b ) 5:3 c)11:7 d)7:3

Explanation: The
sum of the numbers is 72.

The sum of the
terms of the ratio must divide the sum of the numbers.

Taking option 1 :
Sum of the terms = 8+1 = 9 which divides 72.

Taking option 2 :
Sum of the terams = 5 +3 = 8 which divides 72.

Taking option 3:
Sum of the terms = 11 +7 = 18 which divides 72

Taking option 4:
Sum of the terms = 7+3 = 10 which is not factor of 72.

So this cannot the required ratio.

**9.**

**The price of a TV and a Radio are in the ratio of 7:2. If a T.V. costs 25000 more than a Radio, find the price of the T.V.?**

**Explanation :**When TV costs more than the radio by Rs 25000 means , the difference between the price of T.V. and Radio is Rs 25000

Prices
of TV and Radio are in the ratio 7:2. Let their prices be 7x and 2x.

The
difference of their prices => 7x-2x => 5x = Rs 25000=> x= Rs 5000

The
price of the TV => 7x = 7 x 5000 = Rs 35000

**10**.

**Rs 2400 is divided among A, B and C . Half of the A’s share , $\frac{1}{3}$ of the B’s share and $\frac{1}{5}$ th of the C’s share are equal. Then find the share of C?**

**Explanation:**

1
2

A =
1
3

B =
1
5

C are equal. We say they are equal to k

1
2

A =
1
3

B =
1
5

C= k
Therefore A=2k B= 3k and C=5k.

The
ratio of the shares of A,B and C = 2k :3k: 5K= 2:3:5

The share of C = Rs 2400 x

5
10

= Rs 1200**11**.

**Rs 3720 is divided into three parts in proportional to the fractions $\frac{1}{2}$ : $\frac{1}{3}$: $\frac{1}{5}$ . What is the second part?**

**Explanation:**

1
2

:
1
3

:
1
5

=
15
30

:
10
30

:
6
30

The required ratio = 15: 10:6

∴ second part = Rs 3720 x

10
31

=Rs 1200**12.**

**Two numbers are in the ratio of 4:5 and their product is 500.Find the bigger number?**

**Explanation:**Let two numbers be 4x and 5x.

Product
of the numbers =>4x x 5x => 20x

^{2}= 500
=>
x

^{2}= 25 =>x=5
Bigger number = 5x= 5 x 5 = 25

**13**.

**Rs 3120 is divided among A,B and C so that 3 times the A’s share, and twice the B’s share and 4 times of the C’s share are equal. Find the share of A ?**

**Explanation**:

3 times the A’s share, and twice the B’s share and 4 times of the C’s share are equal 3A = 2B= 4C = k

A =

k
3

, B=
k
2

C=
k
4

=> A:B:C =
k
3

:
k
2

:
k
4

A: B : C =

4:6:3
12

The required ratio = 4:6:3

Share
of A = Rs 3120 x

4
13

= Rs 960**14**.

**Rs 7820 are divided among A, B and C so that A receives $\frac{5}{12}$ as much as B and C together receive and B receives $\frac{1}{3}$ as much as A and C together receive. Find the difference between the shares of A and B ?**

**Explanation :**A receives

4
13

as much as B and C
together receive.
A =

5
12

(B+C)=> A : (B+C)= 5:12
A’s
share = Rs 7820 x

5
17

=Rs 2300
B receives

4
13

as much as A and C together
receive
B =

4
13

(A+C)=>
B: (A+C)= 4:13
B’s share = Rs 7820 x

4
17

= Rs 1840
Difference between A and B’s share = Rs 2300 –Rs 1840 =Rs 46013.

15.

15.

**Three numbers are in the ratio 5:4:3 such that the sum of their squares is 0. What is the smallest number?****Explanation:**The numbers are in the ratio of 5:4:3.

Let numbers be 5x,4x and 3x. Given that sum of their squares is 450

Sum of their squares = (5x)

^{2}+(4x)^{2}+(3x)^{2}
ð 25x

^{2}+ 16 x^{2}+ 9 x^{2}= 450
ð 50 x

^{2}=450
ð x

^{2}=9
ð x=3

Smallest number = 3x = 3 x 3 =9