a man buys a piece of land for rupees 384000. he sells two fifths of it at a loss of 6% .at what gain per cent should he sell the remaining piece of land to gain 10% on the whole???
Answers
Step-by-step explanation:
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[
100
100−L%
]
x=\frac{2}{5}\times 384000[\frac{100-6}{100}]x=
5
2
×384000[
100
100−6
]
x=\frac{2}{5}\times384000[\frac{94}{100}]x=
5
2
×384000[
100
94
]
x=\frac{2}{5}\times 384000\times \frac{94}{100}x=
5
2
×384000×
100
94
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+
100
10
×384000=422400
Remaining land is 1-\frac{2}{5}=\frac{3}{5}1−
5
2
=
5
3
In order to sell the land at net 10%gain he should sell the \frac{3}{5}
5
3
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=278016
5
3
×384000+
100
g
×
5
3
×384000=278016
\frac{g}{100}\times\frac{3}{5}\times 384000=47616
100
g
×
5
3
×384000=47616
g=20.66%g=20.66
Therefore, The gain in percentage is 20.66%.
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