Question

A man buys a plot of land at $Rs3,00,000.$ He sells one third of the plot at a loss of 20$\%$ . Again, he sells two -fifth of the plot left at a profit of 25$\%.$ At what price should he sell the remaining plot in order to get a profit of 10$\%$ on the whole?

Answer 1

C.P of the total land$=$Rs.$3,00,000$

Sold ${\frac{1}{3}}^{rd}$ of land at the loss of $20\%$

C.P of ${\frac{1}{3}}^{rd}$ of land$=\frac{1}{3}\times 3,00,000=$Rs$1,00,000$

S.P of ${\frac{1}{3}}^{rd}$ of land$=C.P\times (1-\frac{loss\%}{100})$

$=1,00,000\times (1-\frac{20}{100})=1,00,000\times \frac{80}{100}=$Rs.$80,000‬$

Similarly, sold ${\frac{2}{5}}^{th}$ at a gain of $25\%$ is

C.P of ${\frac{2}{5}}^{th}$ of land$=\frac{2}{5}\times 3,00,000=$Rs.$1,20,000$

S.P of ${\frac{2}{5}}^{th}$ of land$=1,20,000\times (1+\frac{25}{100})$

$=1,20,000\times \frac{125}{100}=$Rs$1,50,000$

Total Gain$\%$ required$=10\%$

Total S.P required$=$Total C.P$\times (1+\frac{Gain\%}{100})$

$=3,00,000\times (1+\frac{10}{100})=3,60,000\times \frac{110}{100}=$Rs.$3,30,000$

S.P of balance land$=3,30,000-80,000-1,50,000=$Rs.$1,00,000$

$\therefore$ he has to sell the balance land at Rs.$1,00,000$