Goods cost Rs. 600 and are sold for Rs. 688.50 on 9 months credit with a 2% true gain. Find the annual simple interest rate.

Given data

• Cost price = Rs. 600
• Credit selling price after 9 months = Rs. 688.50
• True gain = 2% of cost = Rs. 12
• Therefore, required present worth (PW) of proceeds = Rs. 612
• Let annual simple interest rate = r

Concept / Approach

PW = A / (1 + r × t) with t = 9/12 = 0.75 year.

StepsSet 688.50 / (1 + 0.75r) = 6121 + 0.75r = 688.50 / 612 = 1.1250.75r = 0.125 ⇒ r = 0.125 / 0.75 = 0.1666… = 16⅔%

Verification

Final AnswerAnnual rate = 16⅔% p.a.