Question

Sikha spends (\((\frac{1}{3})^{rd}\) of her salary on room rent, \((\frac{1}{4})^{th}\) of the remaining on loan repayment, and \((\frac{1}{5})^{th}\) of the remaining on food. What fraction of her salary is left with her?

• A. \(\frac{1}{5}\)
• B. \(\frac{2}{5}\)
• C. \(\frac{3}{5}\)
• D. \(\frac{4}{5}\)

Answer 1

The Correct Option is B

Step 1: Let Sikha’s total salary be S.

Step 2: Calculate the remaining amount after each expense:

• Room rent: 1/3 of S, so remaining salary: S − S/3 = 2S/3 
• Loan repayment: 1/4 of remaining salary: 1/4 × 2S/3 = 2S/12 = S/6
• Remaining salary after loan repayment: 2S/3 − S/6 = 4S/6 − S/6 = 3S/6 = S/2
• Food expense: 1/5 of remaining salary: 1/5 × S/2 = S/10
• Remaining salary after food expense: S/2 − S/10 = 5S/10 − S/10 = 4S/10 = 2S/5

Final Conclusion: The fraction of salary left with Sikha is 2/5, so the correct answer is (B) 2/5.