Question

Hemant deposits 10% of his salary in PF. He saves 30% of remaining salary. The ratio of his expenses on medicine and groceries is 3 : 4 of remaining salary after saving. If his expenses in medicine was Rs. 2700, then find his monthly salary.

• A. Rs. 30,000
• B. Rs. 20,000
• C. Rs. 10,000
• D. Rs. 15,000

Hint:

When solving problems involving ratios, carefully set up equations for the unknowns and solve step by step.

Answer 1

The Correct Option is C

Let Hemant's monthly salary be \( x \). 

- He deposits 10% of his salary in PF, so the remaining salary is \( 90% \) of \( x \), i.e., \( 0.9x \). 

- He saves 30% of the remaining salary, so the amount saved is \( 0.30 \times 0.9x = 0.27x \). 

- Therefore, the remaining salary after saving is \( 0.9x - 0.27x = 0.63x \). 

The ratio of his expenses on medicine and groceries is 3:4. Let his total expenses on medicine and groceries be \( 0.63x \). 

- Let the amount spent on medicine be \( 3k \) and on groceries be \( 4k \), so: \[ 3k + 4k = 0.63x \] \[ 7k = 0.63x \] \[ k = \frac{0.63x}{7} = 0.09x \] - Since the expenses on medicine are Rs. 2700, we have: \[ 3k = 2700 \] \[ 3 \times 0.09x = 2700 \] \[ 0.27x = 2700 \] \[ x = \frac{2700}{0.27} = 10,000 \] Thus, Hemant's monthly salary is \( \boxed{Rs. 10,000} \).