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?

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Solution

CP of sugar = Rs 4500
Profit on one-third of the sugar = 10%

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

$SP of one - third of the sugar = \frac{100 + gain %}{100} \times CP = Rs \frac{110}{100} \times 1500 = Rs 1650$

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

At a profit of 12%, we have:
$SP of sugar = \frac{100 + gain %}{100} \times CP = Rs \frac{112}{100} \times 4500 = Rs 5040$

∴ 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

$Gain percentage = (\frac{gain}{CP} \times 100) % = (\frac{390}{3000} \times 100) % = 13 %$

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

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