Target gain with 'x for a rupee' pricing Toffees are bought at 8 for a rupee. To gain 60%, at what rate should they be sold?

Introduction / Context:
Items priced as 'x for a rupee' require converting to per-unit cost. To achieve a target gain, compute the necessary per-unit selling price and convert it back to the 'y for a rupee' form.

Given Data / Assumptions:

• CP: 8 for Rs 1 ⇒ CP per toffee = Rs 1/8 = Rs 0.125.
• Target gain = 60% on CP.

Concept / Approach:
Required SP per toffee = CP × (1 + gain%). Then take the reciprocal to express as 'k for a rupee'.

Step-by-Step Solution:
Required SP per toffee = 0.125 × 1.60 = 0.20.'k for a rupee' implies 1/k rupee per toffee = 0.20 ⇒ k = 5.

Verification / Alternative check:
At 5 for Rs 1, SP per toffee = 0.20. Profit per toffee = 0.20 − 0.125 = 0.075. Gain% = 0.075/0.125 × 100 = 60%.

Why Other Options Are Wrong:
6 for Rs 1 yields SP per toffee ≈ 0.1667 (gain < 60%); 9 for Rs 2 ⇒ 0.222... (gain > 60%); 24 for Rs 5 ⇒ ≈ 0.2083 (gain > 60%); 4 for Rs 1 ⇒ 0.25 (too high).

Common Pitfalls:
Adding 60% to the '8' instead of to the price, or inverting the 'k for a rupee' step.

Final Answer:
5 for a rupee