Rakesh deposits 15% of his salary in a fixed deposit, then spends 30% of the remainder on groceries. If cash in hand is ₹ 2380, what is his salary?

Introduction / Context:
This problem chains two percentage operations on the same base (salary). First a fixed-deposit deduction, then an expense from the remainder. The final leftover cash is given; reverse the operations to find the salary.

Given Data / Assumptions:

• Salary = S.
• Fixed deposit = 15% of S ⇒ remainder = 85% of S.
• Groceries = 30% of remainder ⇒ groceries = 0.30 * 0.85S = 0.255S.
• Cash in hand = remainder − groceries = 0.85S − 0.255S = 0.595S = ₹ 2380.

Concept / Approach:
Translate each step to multipliers. The leftover factor after both steps is 0.595. Solve S from 0.595S = 2380. Using fraction 0.595 = 119/200 makes exact arithmetic straightforward.

Step-by-Step Solution:
0.595S = 2380S = 2380 / 0.595 = 2380 * (200/119) = 476000 / 119 = 4000

Verification / Alternative check:
Check forward: FD = 15% of 4000 = 600; remainder = 3400. Groceries = 30% of 3400 = 1020; cash = 3400 − 1020 = 2380. Matches given.

Why Other Options Are Wrong:
35000, 45000, 5000, 4200 are inconsistent with the leftover factor 0.595; substituting them does not yield ₹ 2380 cash.

Common Pitfalls:
Taking 30% of the original salary instead of the remainder, or subtracting percentages additively (15% + 30% = 45%) which ignores compounding on the remainder.

Final Answer:
4000