The ratio of expenditure to savings of a woman is 4 : 1. If her income and expenditure are increased by 20% and 10%, respectively, then find the percentage change in her savings.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 60%.
The ratio of a woman’s expenditure to savings is 4 : 1
Expenditure/Savings = 4/1
Expenditures = 4 × Saving
We know that,
Income = Expenditure + Savings
⇒ Income = 4 × Saving + Savings
⇒ Income = 5 × Savings
Income and expenditure are increased by 20% and 10%, respectively
New income = Income × 120/100
⇒ 5 × Savings × 120/100 = 6 × Savings
New expenditure = Expenditure × 110/100
⇒ 4 × Saving × 110/100 = 4.4 × Savings
Thus,
New Savings = New income - New expenditure
⇒ New Savings = 6 × Savingse - 4.4 × Savings = 1.6 × Savings
So,
Percentage change = (New savings - Old savings)/Old savings × 100
⇒ Percentage change = (1.6 savings - savings)/savings × 100
⇒ 0.6 savings/savings × 100 = 0.6 × 100 = 60%
Thus, The percentage change in her savings is 60%