A man buys a land for Rs. 300000. He sells one - fourth at a loss of 20% and two - fifth at a gain of 25%. At what price must he sell the remaining land so as to make an overall profit of 10%?
Given:
Cost price of the land = Rs. 300000
Loss on one - fourth of land = 20%
Gain on two - fifth of land = 25%
To find: Here we have to find at what price that man must sell the remaining land so as to make an overall profit of 10%.
Solution:
Cost price of total land (CP) = Rs. 300000
So,
CP of $\frac{1}{4}$th land = $\frac{1}{4}$ $\times$ 300000 = Rs. 75000
Given that man sells one - fourth at a loss of 20%;
Selling Price of $\frac{1}{4}$th land = CP of of $\frac{1}{4}$th land $-$ Loss of 20% on CP
Selling Price of $\frac{1}{4}$th land = Rs. 75000 $-$ $(\frac{20}{100} \ \times \ 75000)$
Selling Price of $\frac{1}{4}$th land = Rs. 75000 $-$ 15000
Selling Price of $\frac{1}{4}$th land = Rs. 60000
Also, gain on two - fifth of land is 25%;
CP of $\frac{2}{5}$th land = $\frac{1}{4}$ $\times$ 300000 = Rs. 120000
Selling Price of $\frac{1}{4}$th land = CP of of $\frac{1}{4}$th land $+$ Gain of 25% on CP
Selling Price of $\frac{1}{4}$th land = Rs. 120000 $+$ $(\frac{25}{100} \ \times \ 120000)$
Selling Price of $\frac{1}{4}$th land = Rs. 120000 $+$ 30000
Selling Price of $\frac{1}{4}$th land = Rs. 150000
Now, Calculating SP of total land for overall 10% gain on CP:
SP of total land = CP of total land $+$ Gain of 10% on CP
SP of total land = Rs. 300000 $+$ $\frac{10}{100} \ \times \ 300000$
SP of total land = Rs. 300000 $+$ 30000
SP of total land = Rs. 330000
SP of remaining land = SP of total land $-$ SP of $\frac{1}{4}$th land $-$ SP of $\frac{2}{5}$th land
SP of remaining land = Rs. 330000 $-$ 60000 $-$ 150000
SP of remaining land = Rs. 120000
So, He should sell the remaining plot at Rs. 1,20,000 so as to make an overall profit of 10%.
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