Question

The annual income of A, B and C taken together is Rs 1800. They spend 75%, 85%, and 80% respectively of their incomes. If their annual savings are in the ratio 20:9:8, find the annual savings of each.

Answer 1

Solution:-

Savings ratio = 20 : 9 : 8
Their savings are 20x, 9x and 8x respectively.
It is given that A spends 75 %, B spends 85 % and C spends 80 % of his income.
So, their savings are,
A's savings = 100 - 75
A's savings = 25 %
B's savings = 100 - 85
B's savings = 15 % 
C's savings = 100 - 80 
C's savings = 20 %

A's savings = 20x
⇒ 25 % of A's salary = 20x
⇒ 25/100 × A's salary = 20x
⇒ A's salary = (100/25)*20x
⇒ A's salsry = 80x

B's savings = 9x
⇒ 15 % of B's salary = 9x
⇒ 15/100 × B's salary = 9x
⇒ B's salary = (100/15)*9x
⇒ B's salary = 60x

C's savings = 8x
⇒ 20 % of C's salary = 8x
⇒ 20/100 × C's salary = 8x 
⇒ C's salary = (20/100)*8x
⇒ C's salary = 40x

Total salary of A, B and C = Rs. 1800
So, 
⇒ 80x + 60x + 40x = 1800
⇒ 180x = 1800
⇒ x = 10

Salary of A = 80*10
A's salary = Rs. 800
B's salary = 60*10
B's salary = Rs. 600
C's salary = 40*10
C's salary = Rs. 400

Now, savings of A, B and C
A's savings = 25 % of 800
= (800*25)/100
A's savings = Rs. 200
B's savings = 15 % of 600
= (600*15)/100
B's savings = Rs. 90
C's savings = 20 % of 400
= (400*20)/100
c's savings = Rs. 80
Answer