A man spends 31% and 9% of his monthly income on food and clothing, respectively, and one third of the remaining on the education of children. He saves ₹4,500 per month, which is equal to half the balance after spending on food, clothing and education of children. His monthly salary is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. Rs. 22,500.
Food: 31% of income = 0.31 × income
Clothing: 9% of income = 0.09 × income
Total spent on food and clothing: 0.31 × income + 0.09 × income = 0.4 × income
Remaining income: 100% - 40% = 60% of income
Education spending: (1/3) × remaining income = (1/3) × (60% of income) = 0.2 × income
Total expenses: Food + Clothing + Education = 0.4 × income + 0.2 × income = 0.6 × income
Savings: ₹4,500
Savings are half the balance after expenses: 4,500 = (1/2) × ((100% - 60%) × income)
Simplify: 4,500 = (1/2) × (40% × income)
Rearrange to find income: income = (2 × 4,500)/0.4 = 22,500