Question

A man spends $\frac{2}{5}$ of his salary on house rent, $\frac{3}{10}$ of his salary on food and $\frac{1}{8}$ of his salary on conveyance. If he has Rs. 1400 left with him, find his expenditure on food.

• A. 1000
• B. 2400
• C. 1500
• D. 2000
• E.

Hint:

Always check for simplification and verification by recalculating based on the total to ensure accuracy.

Answer 1

The Correct Option is B

Step 1: Assume the total salary is $x$.
Step 2: The expenses are as follows: - House rent: $\frac{2}{5}x$ - Food: $\frac{3}{10}x$ - Conveyance: $\frac{1}{8}x$ The total expenditure is: $$\frac{2}{5}x + \frac{3}{10}x + \frac{1}{8}x$$ Step 3: Finding the common denominator for the fractions: $$\frac{16}{40}x + \frac{12}{40}x + \frac{5}{40}x = \frac{33}{40}x$$ Step 4: The remaining amount is calculated as follows: $$x - \frac{33}{40}x = \frac{7}{40}x$$ Given that this remaining amount is Rs. 1400: $$\frac{7}{40}x = 1400$$ $$x = 1400 \times \frac{40}{7} = 8000$$ Step 5: The expenditure on food is calculated as: $$\frac{3}{10}x = \frac{3}{10} \times 8000 = 2400$$ Thus, the expenditure on food is Rs. 2400.