Question

A shopkeeper sells $100$ kg of sugar partly at $10\%$ profit and the remaining at $20\%$ profit. If he gains $12\%$ on the whole transaction how much sugar did he sell at $20\%$ profit?

• A. $25$ kg
• B. $40$ kg
• C. $20$ kg
• D. $30$ kg

Answer 1

Answer: (C)

$20$ kg

We take the cost of 1kg of sugar $=$ Rs. $x$

So the price $=100x$.

The shopkeeper sold $20$ kg of sugar at $20\%$ profit.

Then the profit on $100$ kg of sugar at $12\%=$ $100x\times \frac{12}{100}=12x$ .......(i)

Let the sugar be divided into $p$ kg and $(100-p)$ kg.

So the price of $p$ kg $=px$.

Then the profit on $p$ kg at $10\%=$ $px\times \frac{10}{100}=\frac{px}{10}$ ..........(ii).

Again the price of $100-pkg=(100-p)x$.

Then the profit on $(100-p)$ kg at $20\%=$ $(100-p)x\times \frac{20}{100}=\frac{(200-2p)x}{10}$..........(iii).

Then, adding (ii) & (iii), the total profit $=$ $\frac{px}{10}+\frac{(200-2p)}{10}=\frac{x(200-p)}{10}$

$\therefore \frac{x(200-p)}{10}=12x$ ....(comparing with (i))

$\Rightarrow 200-p=120$

$\Rightarrow 100-p=(100-80)$ kg $=20$ kg

So, the shopkeeper sold $20$ kg of rice at $20\%$ profit.