Amal buys 110 kg of syrup and 120 kg of juice, syrup being 20% less costly than juice, per kg. He sells 10 kg of syrup at 10% profit and 20 kg of juice at 20% profit. Mixing the remaining juice and syrup, Amal sells the mixture at â¹ 308.32 per kg and makes an overall profit of 64%. Then, Amal&rsqu

Question

Amal buys 110 kg of syrup and 120 kg of juice, syrup being 20% less costly than juice, per kg. He sells 10 kg of syrup at 10% profit and 20 kg of juice at 20% profit. Mixing the remaining juice and syrup, Amal sells the mixture at â¹ 308.32 per kg and makes an overall profit of 64%. Then, Amal&rsquo;s cost price for syrup, in Rupees per kg, is

Accepted Answer

160 — Easy Let juice cost $10x$/kg so syrup (20% cheaper) costs $8x$/kg — a clean way to handle the $20\%$ gap. Compute the revenue from the small lots sold first, then set total revenue $=1.64	imes$ total cost (the $64\%$ overall profit) to solve for $x$. 1 Set per-kg cost prices. Juice $=10x$, syrup $=20\%$ less $=8x$. 2 Revenue from the lots sold separately: $$\begin{aligned} &10	ext{ kg syrup at }10\%	ext{ profit}=10	imes(8x\cdot1.1)=88x\ &20	ext{ kg juice at }20\%	ext{ profit}=20	imes(10x

CAT 2022 Slot 1 — QA Question 5

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