Question

‘X’ sells fruits at \[21\% \] profit. If X bought it for \[9\% \] less and sold it for Rs. 29 less, he would have gained \[25\% \] . Find the cost price of fruits.

Answer 1

Hint: Let the C.P. of fruits be a. According to the information provided in question, X makes \[21\% \] profit i.e. \[121\% \] of a and \[25\% \] profit, if he bought fruits for \[9\% \] less i.e. \[125\% \] of \[91\% \] of a.
Now, find ‘a’ using ( \[121\% \] of a) – ( \[125\% \] of \[91\% \] of a) = 29.

Complete step-by-step answer:
Let the C.P. of fruits be a.
It is given that, X sells fruits for \[21\% \] profit
So, \[21\% \] profit = \[121\% \] of a.
Also, if X bought fruits for \[9\% \] less i.e. \[91\% \] of a, then he would make \[25\% \] profit.
So, \[25\% \] profit at \[9\% \] less C.P. = \[125\% \] of \[91\% \] of a.
It is also given that, if X bought for \[9\% \] less for \[25\% \] profit, he sold it for Rs. 29 less than original amount.
$\therefore $( \[121\% \] of a) – ( \[125\% \] of \[91\% \] of a) = 29
 \[121\% \] of a \[ = \dfrac{{121}}{{100}} \times a\] and \[125\% \] of \[91\% \] of a \[ = \dfrac{{125}}{{100}} \times \dfrac{{91}}{{100}} \times a\] .
 \[\therefore \left( {\dfrac{{121}}{{100}} \times a} \right) - \left( {\dfrac{{125}}{{100}} \times \dfrac{{91}}{{100}} \times a} \right) = 29\]
 $\therefore \dfrac{{121}}{{100}}a - \dfrac{{11375}}{{10000}}a = 29$
 $\therefore \dfrac{{12100 - 11375}}{{10000}}a = 29$
 $\therefore \dfrac{{725}}{{10000}}a = 29$
 $\therefore a = 29 \times \dfrac{{10000}}{{725}}$
 $\therefore a = 400$
Thus, the C.P. of fruits is Rs. 400.

Note: Any amount of \[\% \] profit, say x \[\% \] , can also be written as \[\left( {100 + x} \right)\% \] of the C.P.
This is because profit is to be added in C.P. to get the total amount. So, we add that x \[\% \] of profit in \[100\% \] of C.P.
Similarly, if it is x \[\% \] loss, we write it at \[\left( {100-x} \right)\% \] .