Answer:

The gain in percentage is 20.66%.                      

Step-by-step explanation:

Given : A man buys a piece of land for rupees 384000. He sells two fifths of it at a loss of 6% .

To find : At what gain per cent should he sell the remaining piece of land to gain 10% on the whole ?

Solution :

The cost price of the land is Rs.384000.

Let the selling price of the land is Rs.x.

He sells two fifths of it at a loss of 6% .

The selling price is SP=CP[\frac{100-L\%}{100}]SP=CP[100100−L%]

x=\frac{2}{5}\times 384000[\frac{100-6}{100}]x=52×384000[100100−6]

x=\frac{2}{5}\times384000[\frac{94}{100}]x=52×384000[10094]

x=\frac{2}{5}\times 384000\times \frac{94}{100}x=52×384000×10094

x=144384x=144384

When there is 10% gain on the whole he should sell at Rs.384000.

So, The price is 384000+\frac{10}{100}\times 384000=422400384000+10010×384000=422400

Remaining land is 1-\frac{2}{5}=\frac{3}{5}1−52=53

In order to sell the land at net 10%gain he should sell the \frac{3}{5}53 of the remaining land at Rs.422400-144384=Rs.278016

Let g be the percentage gain to sell the remaining land

\frac{3}{5}\times 384000+\frac{g}{100}\times\frac{3}{5}\times 384000=27801653×384000+100g×53×384000=278016

\frac{g}{100}\times\frac{3}{5}\times 384000=47616100g×53×384000=47616

g=20.66%g=20.66

Therefore, The gain in percentage is 20.66%.