A man buys a piece of land for ₹ 76800 he sells two fifth of it at a loss of 6% At what gain % he sells it into gain 10% in whole transaction ? please give correct answer and explain .
Answers
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%.