Successive small gains — back-calculating original price through two sales A sells a watch to B at a 5% gain, and B sells it to C at a 4% gain. If C pays Rs 91, what price did A originally pay for the watch?

Introduction / Context:
When an item passes through multiple sellers with gains, reverse the multipliers successively to get back to the earliest cost. Here, we undo B's 4% gain and then A's 5% gain to recover A's original purchase price (his cost price).

Given Data / Assumptions:

• C's payment (final SP) = Rs 91.
• B's gain = 4% ⇒ B's CP = (final SP)/1.04.
• A's gain = 5% ⇒ A's CP = (B's CP)/1.05.

Concept / Approach:
Apply inverse percentage factors because we are moving backward from final selling price to earlier cost prices.

Step-by-Step Solution:
B's cost = 91 / 1.04 = 87.5.A's cost = 87.5 / 1.05 = 83.333... = Rs 83 1/3.

Verification / Alternative check:
Forward check: From 83.333..., A sells at 5% gain ⇒ 87.5. B sells at 4% gain ⇒ 87.5 × 1.04 = 91 exactly.

Why Other Options Are Wrong:
82.81, 83, 84.50, 85 do not reproduce exactly 91 after applying +5% and then +4%.

Common Pitfalls:
Subtracting percent points instead of using multiplicative factors, or applying the percentages on the wrong base and in the wrong order.

Final Answer:
Rs 83.33