Ratios & Proportion [Examples]
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Examples of Ratios —
Example 1:
A sum of money is to be distributed among A, B, C, D in the proportion of 5:2:4:3.
If A gets Rs. 1000 more than C, what is B’s share?
Solution:
Let the share A, B, C, D to be Rs. 5x, Rs. 2x, Rs. 4x, Rs. 3x respectively;
As given is 5x – 4x = 1000 => x = 1000
So B’s share is 2x = 2*1000 = Rs 2000
Example 2:
In a mixture of 60 litres, the ratio of milk and water is 2:1. If this ratio to be changed to 1:2,
then how much more water needs to be added?
A. 60 litres
B. 40 litres
C. 30 litres
D. 20 litres
Solution:
Quantity of milk = (60*(2/3)) litres ⇒ 40 litres
So Quantity of water in mixture = (60- 40) litres ⇒ 20 litres
As New ratio = 1 : 2
As quantity of milk remains same and Let extra quantity of water to be added is x litres.
Then, milk : water = [40/(20 + x)]
So now [40/(20 + x)] = 1/2
⇒ (20 + x) = 80
⇒ x = 60
So quantity of water to add is 60 litres
Alternative solution for competition exams
Given milk:water=2:1 in 60 ltr; so milk=40 ltr and water=20 ltr
New ratio milk:water=1:2
As milk will be same in both the ratios
So, Milk = 1 => 40 ltr
so water = 2 => 40*2 = 80 ltr
left water = 80-20 => 60 ltr
so, 60 ltr water should be added
Example 3:
The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?
Solution:
Let the number of boys and girls in the college be 7x and 8x respectively.
Increased number of boys is = 120% of 7x ⇒ (120/100) * 7x ⇒ (42x)/5
Increased number of boys is = 110% of 8x ⇒ (110/100) * 8x ⇒ (44×0/5
So the final ratio is = (42x/5 : 44x/5) ⇒ 21 : 22
Example 4:
Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each person is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit’s new salary?
Solution:
Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.
With new increase the salaries of Ravi and Sumit is Rs. 2x + 4000 and Rs. 3x + 4000
So from new ratio ⇒ (2x + 4000)/(3x + 4000) = 40/57
⇒ 57*(2x + 4000) = 40*(3x + 4000)
⇒ 57(2x + 4000) = 40(3x + 4000)
⇒ 114x + 57(4000) = 120x + 40 (4000)
⇒ 120x – 114x = 4000(57-40)
⇒ 6x = 4000 (17)
⇒ 3x = 34000
So Sumit’s new salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38000
Examples of Proportions—
Example 1:
If Rs. 782 be divided into three parts, proportional to 1/2 : 2/3 : 3/4, then the first part is?
Solution:
As per the ratio given is 1/2 : 2/3 : 3/4 = 6 : 8 : 9 ( Git this by Multiplying all three parts by 12)
So first part = (782*6/23) ⇒ Rs. 204
Example 2:
The fourth proportional to 5, 8, 15 is?
Solution:
Let the fourth proportional is x then the proportion looks like 5:8:15:x
Then, 5/8 = 15/x
⇒ 5x = (8 * 15)
⇒ 5x = 120
So x = 24