A small bakery makes two types of cakes. Plain cake gives a profit of \rupee 6 per cake and chocolate cake gives a loss of \rupee 4 per cake. If the bakery sells a total of 40 cakes in a day and the net profit is \rupee 80, how many plain and how many chocolate cakes were sold?

Step-by-step solution

1. Let the number of plain cakes be p and chocolate cakes be c.
2. From the total cakes: p + c = 40. $\text{(1)}$
3. Profit equation: 6p - 4c = 80. $\text{(2)}$
4. Multiply (1) by 4 to align coefficients of c: 4p + 4c = 160.
5. Add this result to (2): (6p - 4c) + (4p + 4c) = 80 + 160, giving 10p = 240.
6. Solve for p: p = 240 / 10 = 24. Wait, check arithmetic – the addition should be 6p - 4c + 4p + 4c = 10p, right side 80 + 160 = 240, so p = 24. But p + c = 40, so c = 16. However profit then: 6*24 - 4*16 = 144 - 64 = 80, correct.
7. Thus plain cakes = 24 and chocolate cakes = 16.

Concept tested: Forming equations from word problems

Published 24 August 2026 · How this solution was prepared and checked

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