Amal buys $110 \mathrm{~kg}$ of syrup and $120 \mathrm{~kg}$ of juice, syrup being 20% less costly than juice, per kg. He sells $10 \mathrm{~kg}$ of syrup at 10% profit and $20 \mathrm{~kg}$ of juice at $20 \%$ profit. Mixing the remaining juice and syrup, Amal sells the mixture at Rs. $308.32$ per kg and makes an overall profit of $64 \%$ . Then, Amal's cost price for syrup, in rupees per kg, is

Entered answer:

✅ Correct Answer: 160

Since syrup is 20% less costly than juice, let's set up our variables:

Let cost price of juice = Rs $100x$ per kg

Then cost price of syrup = Rs $80x$ per kg

If juice costs Rs $100x$ , then 20% less would be Rs $100x - 20x = 80x$

This clever choice of variables makes our calculations much easier.

Amal's purchases:

110 kg syrup at Rs $80x$ per kg = Rs $8800x$

120 kg juice at Rs $100x$ per kg = Rs $12000x$

Total Cost Price = Rs $8800x + 12000x = 20800x$

Individual sales:

10 kg syrup at 10% profit = $80x \times 1.1 \times 10 = 880x$

20 kg juice at 20% profit = $100x \times 1.2 \times 20 = 2400x$

Mixed sales:

Remaining syrup = $110 - 10 = 100$ kg

Remaining juice = $120 - 20 = 100$ kg

Total mixture = 200 kg at Rs $308.32$ per kg = Rs $61664$

Total Selling Price = Rs $880x + 2400x + 61664 = 3280x + 61664$

Amal makes an overall profit of 64%.

This means: Selling Price = Cost Price $\times 1.64$

So: Selling Price = $20800x \times 1.64 = 34112x$

Now we can equate our two expressions for selling price:

$34112x = 3280x + 61664$

$30832x = 61664$

$x = \tfrac{61664}{30832} = 2$

Cost price of syrup = $80x = 80 \times 2 = 160$ per kg

We used smart variable choice (using $80x$ and $100x$ ) to eliminate fraction calculations. We tracked quantities carefully by separating individual sales from mixed sales. We used overall profit percentage as a checking mechanism.

The answer is Rs 160 per kg.

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