Average cost of 5 apples and 4 mangoes is Rs. 36. The average cost of 7 apples…

Concept: Average cost of a group of items equals the total cost of the group divided by the number of items in it. When two such average-based total-cost equations combine, by direct addition, to produce exactly the required linear combination of the unknowns (apple-cost plus mango-cost), that combination can be found without solving for each unknown separately.

1. Let the cost of one apple be a and the cost of one mango be m.

2. The average cost of 5 apples and 4 mangoes (9 items) is Rs. 36, so the total cost is 9 × 36 = Rs. 324. This gives 5a + 4m = 324.

3. The average cost of 7 apples and 8 mangoes (15 items) is Rs. 48, so the total cost is 15 × 48 = Rs. 720. This gives 7a + 8m = 720.

4. Adding the two equations: (5a + 4m) + (7a + 8m) = 324 + 720, which gives 12a + 12m = 1044.

5. Dividing by 12: a + m = 87, the combined cost of one apple and one mango together.

6. The required cost of 24 apples and 24 mangoes is 24a + 24m = 24(a + m) = 24 × 87 = Rs. 2088.

Cross-check: doubling the combined-equation total directly, 2 × 1044 = 2088, matches the same result obtained via a + m = 87, confirming the answer through two independent routes.

Hence, the total cost of 24 apples and 24 mangoes is Rs. 2088.