Question

Ahmed buys a plot of land for Rs. 480000. He sells $\dfrac{2}{5}$ of it at a loss of 6 %. At what gain percent should he sell the remaining part of the plot to gain 10 % on the whole?

Answer 1

Hint:First of all, find the $S{{P}_{1}}$ such that gain % would be 10 % on the whole. Now, find $S{{P}_{2}}$ at which he sold $\dfrac{2}{5}$ of the land at 6 % loss. Now subtract $S{{P}_{2}}\text{ from }S{{P}_{1}}$ to get $S{{P}_{3}}$. Also, subtract $C{{P}_{2}}\text{ of }\dfrac{2}{5}$ of the land from the total $C{{P}_{1}}\text{ to get }C{{P}_{3}}$. Now, find the gain % using $\left( \dfrac{S{{P}_{3}}-C{{P}_{3}}}{C{{P}_{3}}} \right)\times 100$.

Complete step-by-step answer:
We are given that Ahmed buys a plot of land for Rs. 480000. He sell $\dfrac{2}{5}$ of it at a loss of 6 %. We have to find the gain percent at which he should sell the remaining part of the plot to gain 10 % on the whole.
Now, let us consider our question. We are given that Ahmed buys a plot of Rs. 48000. So, we get,
$\text{Total }C{{P}_{1}}=Rs.480000.....\left( i \right)$
We are given that the total gain % should be 10 %. We know that,
Gain % = $\left( \dfrac{S.P-C.P}{C.P} \right)\times 100$
By substituting
$CP=C{{P}_{1}}=Rs.480000$
Gain % = 10 %
$SP=S{{P}_{1}}$
We get,
$10=\dfrac{\left( S{{P}_{1}}-480000 \right)}{480000}\times 100$
$48000=S{{P}_{1}}-480000$
$S{{P}_{1}}=480000+48000$
So, we get,
$S{{P}_{1}}=Rs.528000....\left( ii \right)$
He sells $\dfrac{2}{5}$ of it at a loss of 6 %. So, we get, CP of $\dfrac{2}{5}$ of the plot
$=C{{P}_{2}}=\dfrac{2}{5}\times 480000$
So, we get,
$C{{P}_{2}}=2\times 96000=Rs.192000....\left( iii \right)$
We know that,
Loss % $=\left( \dfrac{CP-SP}{CP} \right)\times 100$
By substituting
$CP=C{{P}_{2}}=Rs.192000$
Loss % = 6 %
$SP=S{{P}_{2}}$
We get,
$6=\left( \dfrac{192000-S{{P}_{2}}}{192000} \right)\times 100$
$6\times 1920=192000-S{{P}_{2}}$
So, we get,
$S{{P}_{2}}=192000-11520$
$S{{P}_{2}}=Rs.180480....\left( iv \right)$
So, we have got the total CP that is $C{{P}_{1}}=Rs.480000\text{ and }C{{P}_{2}}=Rs.192000$
So, we get CP of the remaining that is
$C{{P}_{3}}=C{{P}_{1}}-C{{P}_{2}}$
$C{{P}_{3}}=Rs480000-Rs.192000$
$C{{P}_{3}}=Rs288000.....\left( v \right)$
We have also got the total SP that is $S{{P}_{1}}=Rs.528000,S{{P}_{2}}=Rs.180480$. So, we get, SP of the remaining part, that is,
$S{{P}_{3}}=S{{P}_{1}}-S{{P}_{2}}$
$S{{P}_{3}}=Rs.528000-Rs.180480$
$S{{P}_{3}}=Rs.347520...\left( vi \right)$
We know that,
Gain % = $\left( \dfrac{S.P-C.P}{C.P} \right)\times 100$
So, we get, the gain % of the remaining part,
$=\dfrac{\left( S{{P}_{3}}-C{{P}_{3}} \right)}{C{{P}_{3}}}\times 100$
$=\dfrac{\left( 347520-288000 \right)}{288000}\times 100$
$=\dfrac{59520}{288000}\times 100$
= 20.6667 %
So, we get the gain percent of the remaining part as 20.67 %.

Note: In these types of questions, always take care of taking the SP and CP of the same part or the same quantity. For example, if the CP is of the $\dfrac{2}{5}th$ part, that is, SP should also be of $\dfrac{2}{5}th$ part only. Also, students must understand that the physical significance of the profit and loss is that when SP > CP, profit is increased while when CP > SP, there is a loss. Students should also remember that we see loss, loss %, profit %, etc. with respect to CP.