Question

Mariyam bought some Black pencils at the rate of Rs.$5$ per $9$ pencils and an equal number of coloured pencils at the rate of Rs. $5$ per $11$ pencils. If she sold all the pencils at the rate of Rs.$5$ per $10$ pencils, the gain or loss percent is –
A.No gain or no loss
B.gain$1\% $
C.loss$10\% $
D.loss$1\% $

Answer 1

Hint: If selling price is greater than cost price then profit occurs. If selling price is less than cost price then loss occurs. Then use formula of loss% if loss occurs which is-
$ \Rightarrow {\text{Loss% = }}\dfrac{{C.P. - S.P.}}{{C.P.}} \times 100$
If profit occurs use the formula of profit% which is-
$ \Rightarrow {\text{Gain% = }}\dfrac{{S.P. - C.P.}}{{C.P.}} \times 100$

Complete step-by-step answer:
Given, Cost price of $9$ black pencils =$Rs.5$
Then the cost price of one black pencil =$\dfrac{5}{9}$ Rs.
Also the cost of $11$ coloured pencils=$Rs.5$
Then the cost price of one coloured pencil=$\dfrac{5}{{11}}$ Rs.
Then total cost price of two types of pencils=cost price of black pencils cost price of colored pencils
Total cost price of two pencils=$\dfrac{5}{9} + \dfrac{5}{{11}}$
On taking LCM, we get
Total cost price of all pencils=$\dfrac{{55 + 45}}{{99}} = \dfrac{{100}}{{99}}$
Now the selling price of $10$ pencils=$Rs.5$
Then selling the price of one pencil=$\dfrac{5}{{10}} = \dfrac{1}{2}$ Rs.
Here since she sells two types of pencils, one black and one coloured then
Selling price of the two pencils=$\dfrac{1}{2} \times 2 = 1$
We have to find the loss or gain percentage.
Here since $\dfrac{{100}}{{99}} > 1$ which means the cost price is greater than the selling price so loss occurs.
And we know the formula of loss % is
$ \Rightarrow {\text{Loss% = }}\dfrac{{C.P. - S.P.}}{{C.P.}} \times 100$
On putting the given values we get,
$ \Rightarrow $ Loss%=$\dfrac{{\dfrac{{100}}{{99}} - 1}}{{\dfrac{{100}}{{99}}}} \times 100$
On solving we get,
$ \Rightarrow $ Loss%=$\dfrac{{\dfrac{{100 - 99}}{{99}}}}{{\dfrac{{100}}{{99}}}} \times 100 = \dfrac{{\dfrac{1}{{99}}}}{{\dfrac{{100}}{{99}}}} \times 100$
On simplifying we get,
$ \Rightarrow $ Loss%=$\dfrac{1}{{100}} \times 100 = 1$
Hence Mariyam incurs $1\% $ loss.
Hence the correct answer is D.

Note: Here we have calculated the selling price for two pencils because the total cost price is also of two pencils; one coloured and one black. If we calculated the selling price for only one pencil then we will get the wrong answer.