A man buys a plot of land for $300000$ . He sells $1 / 3$ at a loss of $20 %$ and $2 / 5 t h$ at a gain of $25 %$ . At what price must he sell the remaining land so as to make a profit of $10 %$ on remaining part.

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Solution

Let the cost of agriculture land be $x$ .
A man buys a plot of agricultural land for $R s 300000.$
Cost price of $x = R s .300000 .$

Cost price of $\frac{1}{3} x = \frac{1}{3} \times 300000 = 100000$ .

He sells one third at a loss of $20 %$ .

Selling price is given by,
$S P = C P (1 - \frac{L o s s %}{100})$

$= 100000 (1 - \frac{20}{100}) = 80000$

Cost price of $\frac{2}{5} x$ is $\frac{2}{5} x \times 300000 = 120000$

He sells two fifths at a gain of $25 %$ .

Selling price is given by,
$S P = C P (1 + \frac{p r o f i t %}{100})$

$= 120000 (1 + \frac{25}{100}) = 150000$

Remaining land $= x - \frac{1}{3} x - \frac{2}{5} x = \frac{4 x}{15}$

Cost price of $\frac{4}{5} x$ is $\frac{4}{15} \times 300000 = 80000$

He sell the remaining land so as to make an overall profit of $10 %$ .

Selling price is given by,
$S P = C P (1 + \frac{P %}{100})$

$S P = 80000 (1 + \frac{10}{100})$

$S P = 80000 (1 + 0.1)$

$S P = 80000 \times 1.1$

$S P = 88000$

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A man buys a plot of land at $R s . 3, 60, 000$ . He sells one third of the plot at a loss of $20 %$ . Again, he sells one-third 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?