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
b2
a
Third proportion of 18 and 12 =
122
18
= 8
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 1st
part?
Explanation:: Divided in the ratio= 5:4
Sum of the parts= 5+4= 9
Sum of the parts= 5+4= 9
1st 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:
We say they are equal to k
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 => 20x2 = 500
=>
x2 = 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
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. Three numbers are in the ratio 5:4:3 such that the sum of their squares is 0. What is the smallest number?
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 25x2 + 16 x2 + 9 x2 = 450
ð 50 x2 =450
ð x2=9
ð x=3
Smallest number = 3x = 3 x 3 =9