The total income of three families is ₹72,000. Their expenditures are 80%, 85% and 75%, respectively. If the savings are in the ratio 8 : 9 : 20, then the income of the second family is:
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Correct answer: D
Explanation
The correct answer is Option 4 i.e. ₹24,000.
The total income of three families is ₹72,000and their expenditures are 80%, 85% and 75%, respectively
We know that,
Savings = Income - Expenditure
For the first family
Savings(S1) = I1 - 0.80 I1 = 0.20 I1
Savings(S2) = I2 - 0.85 I2 = 0.15 I2
Savings(S3) = I3 - 0.75 I3 = 0.25 I3
The savings are in the ratio 8 : 9 : 20
⇒ 0.20 I1/0.15 I2 = 8/9
⇒ 20 I1/15 I2 = 8/9
⇒ I1/I2 = 2/3 and,
⇒ I1/I3 = 1/2 and,
⇒ I3/I2 = 4/3
The total income = I1 + I2 + I3 = 72000
⇒ 2I2/3 + I2 + 4I2/3 = 72000
⇒ (2I2 + 3I2 + 4I2)/3 = 72000
⇒ 9I2/3 = 72000
⇒ I2 = 72000/3
⇒ I2 = 24000
Thus, The income of the second family is ₹24,000