Question

A man sells two wrist watches at 594 each. On one he gains 10% and on the other he loses 10%. Find his gain or loss percent on the whole.

Answer 1

Hint: From the above question we need to find the cost price and compare it with the selling price. We need to find the cost price with the given percentages of loss and gain. It concludes whether it was a loss or gain. Then we can calculate the gain/loss percentage using${\text{Gain/Loss% = }}\dfrac{{{\text{Gain/Loss}}}}{{{\text{Cost Price}}}} \times 100$

Complete step-by-step solution -
Given, one wrist watch cost will be Rs 594
Then 2 wrist watches cost = 594 x 2 = Rs 1188
Therefore Selling Price of the wrist watches = Rs.1188
Given, He gains 10% by selling the wrist watch.
Therefore, Gain = 10%
The selling price can be given by
$ \Rightarrow $Selling Price = Cost Price + Gain
Let the cost price be 100%
Therefore, Selling Price$ = 100 + 10 = 110\% $
Therefore, This percentage 110% = Rs 594
$ \Rightarrow 1\% = \dfrac{{594}}{{110}} = {\text{ Rs}}{\text{. }}5.40$
$ \Rightarrow 100\% = 5.40 \times 100 = {\text{Rs}}{\text{. }}540$
The cost price of the one he losses 10%:
Therefore, Loss = 10%
Selling Price = Cost Price - Loss
Selling Price $ = 100 - 10 = 90\% $
This percentage 90% = Rs 594
$ \Rightarrow 1\% = \dfrac{{594}}{{90}} = {\text{ Rs}}{\text{. 6}}{\text{.60}}$
$ \Rightarrow 100\% = 6.60 \times 100 = {\text{Rs}}{\text{. 66}}0$
The total cost price:
Total cost price $ = 540 + 660 = {\text{Rs}}{\text{. 1200}}$
The profit / loss can be given by
Profit: The profit or gain is equal to the selling price minus cost price.
Loss: The loss is equal to the cost price minus selling price.
Since$1200 > 1188$
$ \Rightarrow $ Cost Price > Selling Price
$ \Rightarrow $ It is a Loss
Therefore, Loss $ = 1200 - 1188 = {\text{Rs}}{\text{. 12}}$
The Loss percentage:
Loss Percentage$ = \dfrac{{{\text{Loss}}}}{{{\text{Cost Price}}}} \times 100$
Loss Percentage $ = \dfrac{{12}}{{1188}} \times 100 = \dfrac{{100}}{{99}} = 1.01\% $
Therefore, The loss percentage$ = 1\% $


Note: In this problem we have faced the loss. If the solution turned out to be gain, then we need to calculate the gain percentage by using${\text{Gain% = }}\dfrac{{{\text{Gain}}}}{{{\text{Cost Price}}}} \times 100$where gain can be calculated by using ${\text{Gain = Selling Price - Cost Price}}$