Ahmed buys a plot of land for ₹ 480000. He sells of it at a loss of 6%. At what gain per cent should he sell the remaining part of the plot to gain 10% on the whole?

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Solution

CP of the plot of land = ₹4,80,000
CP of $\frac{2}{5}$ th of the land = $\frac{2}{5} \times 480000 = ₹ 1, 92, 000$
Loss on $\frac{2}{5}$ th of the land = 6%
SP of $\frac{2}{5}$ th of the land = CP − Loss
$= 192000 - \frac{6}{100} \times 192000 = ₹ 1, 80, 480$
CP of $\frac{3}{5}$ th of the land = 480000 − 192000 = ₹2,88,000
Total gain% = 10%
Total gain = $\frac{10}{100} \times 480000 = ₹ 48, 000$
Total SP = CP + Gain = ₹4,80,000 + ₹48,000 = ₹5,28,000
SP of $\frac{3}{5}$ th of the land = ₹5,28,000 − ₹1,80,480 = ₹3,47,520
Gain on $\frac{3}{5}$ th of the land = SP of $\frac{3}{5}$ th land − CP of $\frac{3}{5}$ th land
= ₹3,47,520 − ₹2,88,000
= ₹59,520
Gain% on seling the remaining part of the plot = $\frac{Gain}{CP of \frac{3}{5} th land} \times 100 % = \frac{59520}{288000} \times 100 % = 20 \frac{2}{3} %$

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