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?

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?

Vedantu Content Team · Accepted Answer

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.