Question

A mixture of coffee and cocoa, 16% of which is coffee, costs Rs 240 per kg. Another mixture of coffee and cocoa, of which 36% is coffee, costs Rs 320 per kg. If a new mixture of coffee and cocoa costs Rs 376 per kg, then the quantity, in kg, of coffee in 10 kg of this new mixture is:

• A. \(2.5\)
• B. \(5\)
• C. \(4\)
• D. \(6\)

Hint:

When mixtures of the same two ingredients are given with different compositions and costs, set up linear equations using the percentage of each ingredient and solve for the individual prices. Then use those prices to find the composition of any new mixture.

Answer 1

The Correct Option is B

Step 1: Compare the two given mixtures: raising the coffee share from 16% to 36% (a 20-point jump) raises the price from 240 to 320, a jump of Rs 80. So price rises steadily as coffee share rises.
Step 2: Check the options directly by converting each one's coffee amount (out of 10 kg) into a coffee percentage and seeing which is consistent with the given prices. Option 2 says 5 kg coffee, i.e. 50% coffee.
Step 3: A 50% mixture is 14 points beyond mixture 2's 36%; scaling the same rate of price rise (Rs 80 per 20 points, i.e. Rs 4 per point) gives an extra \(14\times4=56\), so price \(=320+56=376\) — exactly matching. No other option (2.5 kg, 4 kg or 6 kg coffee) reproduces 376 this way.
\[ \boxed{5 \text{ kg}} \]