**Question:**

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?

**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 $=\frac{\text { Gain }}{\text { CP of } \frac{3}{5} \text { th land }} \times 100 \%=\frac{59520}{288000} \times 100 \%=20 \frac{2}{3} \%$