Question

A man sold two articles for Rs 3000 each gaining 20% on the one and losing 20% on the other. Find his gain or loss percent on the whole transaction.

Answer 1

Hint-In such questions we use the concept of profit and loss. Find out the sum total of cost price and the selling price of both the articles. Then the sum total of selling price has to be subtracted from the sum total of cost price to get the desired loss. Using the percentage formula you can get the loss percentage on the whole transaction.

Complete step-by-step answer:
$ \Rightarrow $ Total selling price = Rs 3000 + Rs 3000 = Rs 6000
Cost price of the first article which was sold at a gain of 20%
$ \Rightarrow $ $SP = \dfrac{{\left( {100 + gain\% } \right)}}{{100}} \times CP$
$ \Rightarrow $ $3000 = CP \times \left( {1 + \dfrac{{20}}{{100}}} \right)$ ( where 20 is the gain percentage and 3000 is the SP )
$ \Rightarrow $ $CP = 3000 \times \dfrac{{100}}{{120}} = Rs2500$
Similarly cost price of the second article which was sold at a loss of 20%
 = $\dfrac{{3000 \times 100}}{{80}} = Rs3750$
$ \Rightarrow $ Total cost price = Rs 2500 + Rs 3750 = Rs 6250
Thus there is a loss which is equal to cost price – selling price
= Rs 6250 – Rs 6000 = Rs 250
Loss percentage =$\dfrac{{loss}}{{TCP}} \times 100$, where CP is the Total Cost Price.
$ \Rightarrow $ $\dfrac{{250}}{{6250}} \times 100 = 0.04 \times 100 = 4\% $

Note – In such types of questions the key thing to remember is to always recall all the properties and formulas of profit and loss, using these formulas we can easily find gain or loss percent.