Question

Some lollipops are bought at 11 for a rupee and the same number at 9 rupee. If the lot is sold at 10 a rupee, find the gain or loss percent.
A) 2% gain
B) 2% loss
C) 1% gain
D) 1% loss

Answer 1

Hint: The above question is based on the concept of profit or loss. The main approach towards solving the above question is to first find out the total cost price of the lollipops and also the total selling price after selling. Depending on the values of cost price and selling price we can find the gain or loss percent.

Complete step-by-step solution:
Profit and loss help us in understanding whether a commodity or business is profitable or not. In the above given question, the commodity is lollipop where it was bought for one rupee for 11.
Therefore for 11 lollipops the cost is 1 rupee.
Then for 1 cost is \[\dfrac{1}{{11}}\].
Therefore for 11 lollipops the cost is 1 rupee.
And for 9 lollipops the cost is 1 rupee.
Then for 1 lollipop the cost will be \[\dfrac{1}{9}\].
The total cost price is \[\dfrac{1}{{11}} + \dfrac{1}{9} = \dfrac{{20}}{{99}}\]Rs.
Now if the lot is sold at 1-rupee for10.
Then selling price of 1 lollipop is \[\dfrac{1}{{10}}\]
Selling prices for 2 numbers= \[2 \times \dfrac{1}{{10}} = \dfrac{1}{5}\]Rs.
Therefore,
Loss=Cost price-Selling price
\[\dfrac{{20}}{{99}} - \dfrac{1}{5} = \dfrac{1}{{495}}\]
Now calculating Loss percent,
\[Loss\% = \dfrac{{Loss}}{{CP}} \times 100 = \dfrac{{\dfrac{1}{{495}}}}{{\dfrac{{20}}{{99}}}} \times 100 = 1\% \]

So, the loss percent is \[1\% \].

Note: An important thing to note is that the loss or profit depends on the value of cost price or selling price.If the selling price is greater than cost price then it is profit and its cost price is greater than selling price than it is a loss.