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

Answer 1

The Correct Option is B

Step 1: Let the total salary be \( x \).

Step 2: The expenditures are given as: 

• 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 a 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:

\[ x - \frac{33}{40}x = \frac{7}{40}x \]

Given that this remaining amount is Rs. 1400, we set up the equation:

\[ \frac{7}{40}x = 1400 \]

Solving for \( x \):

\[ x = \frac{1400 \times 40}{7} = 8000 \]

Step 5: The expenditure on food is:

\[ \frac{3}{10}x = \frac{3}{10} \times 8000 = 2400 \]

Thus, the correct answer is Rs. 2400.