Inferring the annual interest rate from a credit sale gain: Vandana bought a watch for ₹ 600 and sold it the same day for ₹ 688.50 on 9 months’ credit. She states this way she “gained 2%.” Find the simple-interest rate per annum implicit in this credit sale.

Introduction / Context:
When a seller quotes a future-dated price but claims a particular gain percent “today,” it means the present worth of the credit price equals the cost inflated by the gain percent. Use true-discount present worth to infer the implicit simple-interest rate for the credit period.

Given Data / Assumptions:

• Cost price (cash) = 600.
• Quoted selling price for 9 months = 688.50.
• Claimed gain = 2% on cost, interpreted “as of today.”

Concept / Approach:
Present worth PW of future SP at rate r for t years satisfies PW = SP / (1 + r * t). Since the seller gained 2% today, PW must equal 600 * 1.02 = 612. Solve for r with t = 9/12 = 0.75.

Step-by-Step Solution:
PW = 612 = 688.50 / (1 + r * 0.75).1 + 0.75r = 688.50 / 612 = 1.125.0.75r = 0.125 ⇒ r = 0.125 / 0.75 = 1/6 = 0.166666… = 16 2/3% p.a.

Verification / Alternative check:
Check discount factor at r = 1/6: 1 + r * t = 1 + (1/6) * (3/4) = 1 + 1/8 = 1.125; 688.50 / 1.125 = 612, matching the required today's value.

Why Other Options Are Wrong:

• 15 2/3%, 11 2/3%, 5 2/3% produce present worths different from 612.

Common Pitfalls:

• Treating 688.50 as cash today instead of a future amount and computing (688.50 − 600)/600.

Final Answer:
162/3%