Profit and Loss [लाभ और हानि]–09

Question: A man sold a book at a loss of 7%. Had he been able to sell it at a gain of 9%, it would have fetched Rs.64 more. Find the cost price. [एक व्यक्ति एक किताब को 7% हानि पर बेचता है. यदि वह इस किताब को 9% लाभ पर बेचने में सफल हो गया होता, तो उसे 64 रु ज्यादा मिलते. किताब का क्र्यमूल्य बताएं.] [Ans. (e) None of these (Rs. 400)]

(a) Rs.350 (b) Rs.500 (c) Rs.300   (d) Rs.475 (e) None of these
Solution:

Detailed Explanation: Cost Price (CP) is always taken as 100%. Since the difference between a loss of 7% and a profit of 9% is 16% and the difference between the Selling Prices (SP) is Rs. 64.

It can also be understand as:

When the book is sold at a loss of 7%, then the selling price is 93% and when it is sold at a profit of 9%, then the selling price is 109%. The difference between the selling prices is 109%-93% = 16%  

Therefore, 16% ≡ Rs. 64

Or, 100% ≡? = Rs. 400 Ans.

In other words, 16% of principal = Rs. 64

Or, principal = Rs. (64 × 100) ÷ 16 = Rs. 400. Ans.