The cost of two dozen apples and three dozen bananas is ₹ 136. The cost of 5 dozen bananas and one dozen apples is ₹ 110. What is the price of one dozen bananas?

### Concept & Strategy This is a classic word problem requiring translation into a system of linear equations. Since the question asks for the price of a "dozen" bananas and provides all quantities in "dozens", we do not need to convert to individual items (i.e., do not multiply or divide by 12). ### Step-by-Step Solution **Given:** Let the price of one dozen apples be $A$ and one dozen bananas be $B$. 1. $2A + 3B = 136$ 2. $1A + 5B = 110$ **Calculation:** * We need to find $B$ (bananas). The easiest path is to use the substitution method since Equation 2 has a solitary $A$. * Isolate $A$ in equation (2): $A = 110 - 5B$ * Substitute this expression for $A$ into equation (1): $2(110 - 5B) + 3B = 136$ * Expand and solve for $B$: $220 - 10B + 3B = 136$ $220 - 7B = 136$ $-7B = 136 - 220$ $-7B = -84$ $B = \frac{84}{7} = 12$ * The cost of one dozen bananas is ₹ 12. ### Exam Strategy & Shortcut Alternatively, use the Elimination Method if you prefer to avoid negative numbers. Multiply the second equation by 2 to align the $A$ terms: $2A + 10B = 220$ $2A + 3B = 136$ Subtract vertically: $7B = 84 \implies B = 12$. This requires slightly less algebraic manipulation and prevents sign errors. ### Common Pitfall The most dangerous pitfall here is unnecessary unit conversion. Because the word "dozen" is used, students often reflexively divide the total prices by 12 to find the cost of a single apple or banana, which creates messy fractions and drastically increases solving time. Always match your variables to the units requested in the final question. ### Final Answer **Therefore, the correct answer is None of these.**