**Question:**

A grocer bought sugar worth Rs 4500. He sold one-third of it at a gain of 10%. At what gain per cent must the remaining sugar be sold to have a gain of 12% on the whole?

**Solution:**

CP of sugar = Rs 4500

Profit on one-third of the sugar $=10 \%$

CP of one-third of the sugar $=$ Rs $\frac{4500}{3}=$ Rs. 1500

SP of one $-$ third of the sugar $=\frac{100+\text { gain } \%}{100} \times \mathrm{CP}$

$=\mathrm{Rs} \frac{110}{100} \times 1500$

$=\mathrm{Rs} 1650$

Now, profit= Rs (1650 − 1500) = Rs 150

At a profit of 12%, we have:

SP of sugar $=\frac{100+\text { gain } \%}{100} \times \mathrm{CP}$

$=$ Rs $\frac{112}{100} \times 4500$

$=$ Rs 5040

∴ Gain= Rs (5040 − 4500) = Rs 5400

Profit on the remaining amount of sugar = Rs (540 − 150) = Rs 390

CP of the remaining sugar = Rs (4500 − 1500) = Rs 3000

Gain percentage $=\left(\frac{\text { gain }}{\mathrm{CP}} \times 100\right) \%$

$=\left(\frac{390}{3000} \times 100\right) \%$

$=13 \%$

Therefore, the profit on the remaining amount of sugar is 13%.