A, B and C spend 80%, 85% and 75% of their incomes, respectively. If their savings are in the ratio 8 : 9 : 20 and the difference between the incomes of A and C is Rs. 18,000, then the income of B is:

Solution (By Examveda Team)

Given:
A, B, and C spend 80%, 85%, and 75% of their incomes respectively.
Savings are in the ratio 8 : 9 : 20 respectively.
Difference between the income of A and C is Rs. 18,000.
Concept used:
Income - Expenditure = Savings
Calculation:
A, B and C spend 80%, 85% and 75% of their incomes respectively.
Out of 100%, A spend 80%,
Income : Expenditure = 100 : 80 = 5 : 4,
Out of 100%, B spend 85%,
Income : Expenditure = 100 : 85 = 20 : 17,
Out of 100%, C spend 75%,
Income : Expenditure = 100 : 75 = 4 : 3,
Ratio Income : Expenditure is 5 : 4, 20 : 17, 4 : 3 respectively.
Savings = Income - Expenditure
Savings of A : B : C = (5 - 4) : (20 - 17) : (4 - 3)
Savings of A : B : C = 1 : 3 : 1
According to the question,
Savings are in the ratio 8 : 9 : 20 respectively.
Adjusting the savings ratio,
⇒ Savings = 1 × 8 : 3 × 3 : 1 × 20 = 8 : 9 : 20
⇒ Income = 5 × 8 : 20 × 3 : 4 × 20 = 40 : 60 : 80
⇒ Expenditure = 4 × 8 : 17 × 3 : 3 × 20 = 32 : 51 : 60
According to the question,
Income of C - Income of A = 18,000
⇒ 80 - 40 = 18,000
⇒ 1 unit = $$\frac{{18,000}}{{40}}$$  = 450
Income of B = 60 unit
⇒ 60 × 450 = Rs. 27,000
∴ The income of B is Rs. 27,000.