A man deposits 10% of his salary in PF. He saves 30% of the remaining amount,…

Concept

When a salary is reduced step by step (a deduction, then a saving on what is left, then a split of the final remainder), each later quantity is a fraction of the running balance, not of the original salary. Work with the remaining balance after each step: multiply the surviving fraction at each stage, then apply the part-to-whole ratio to that final balance.

Application

Let the monthly salary be S.

1. PF deduction is 10% of S, so the balance left is 90% of S = 0.9S.

2. He saves 30% of this balance, so the amount that survives saving is 70% of 0.9S = 0.7 × 0.9S = 0.63S.

3. This 0.63S is split between medicine and groceries in the ratio 3 : 4, i.e. 7 equal parts. The medicine share is 3 of those 7 parts = (3/7) × 0.63S = 0.27S.

4. Medicine expense is given as Rs 2700, so 0.27S = 2700, which gives S = 2700 ÷ 0.27 = Rs 10,000.

Cross-check

Substitute S = 10,000 back: PF balance = 9000; after 30% saving the remainder = 6300; the 3 : 4 split of 6300 gives medicine = (3/7) × 6300 = 2700 and groceries = (4/7) × 6300 = 3600. The medicine figure matches the given Rs 2700, so the monthly salary is Rs 10,000.