Concept of “Profit and Loss”–13

Question: A man buys two horses for Rs.1350. He sells one so as to loss 6% and the other to gain 7.5%. On the whole he neither gains nor loses. What is the cost of the horse sold at a loss of 6%.  [Ans. (b) Rs.750]

(a) Rs.500 (b) Rs.750 (c) Rs. 760 (d) Rs.800 (e) None of these

Solution:

Detailed Explanation: 

First Method: The given question can be solved by method of “Alligation”. The first horse is sold at a loss of 6%, while another horse is sold at a profit of 7.5%. On the whole he neither gains, nor losses.

The ratio of the CP of the horse is (7.5-0) : {0 – (- 6)} = 7.5:6 = 5: 4

Total CP is given as Rs. 1350, which is the sum of 5 and 4, that is, 9

So, 9 ≡ Rs. 1350

Or, 5 ≡? = Rs. 750 Ans.

                            Solution: First Method    

                          By method of Alligation,

                          I (%)                       II (%)

                          - 6                            7.5   

                                         Mean (%)                   

                                             0

                          7.5               :             6  

                          Or, 5           :             4   

                              So, 9 ≡ Rs. 1350

                                     5 ≡? = Rs. 750 Ans.

Second Method: Let “x” and “y” are respectively the cost prices of the horses sold at a loss of 6% and a profit of 7.5%.

Given that the sum of the cost prices is Rs. 1350

So, x + y = 1350

Also given that the numerical value of the loss is equal to the numerical value of profit. That is, in the whole transaction, the man neither gains nor losses.

So, 6% of x = 7.5% of y

or, x: y= 5: 4

9 ≡ Rs. 1350 [Since total profit is Rs. 1350]

5 ≡? = Rs. 750 Ans. [5 represents the CP of the horse sold at 6% loss]