8 oranges cost as much as 5 apples, 5 apples as much as 3 mangoes, 4 m

8 oranges cost as much as 5 apples, 5 apples as much as 3 mangoes, 4 mangoes as much as 8 pineapples. If 3 pineapples cost Rs. 36, then an orange’s cost is :

Rs. 9
Rs. 12
Rs. 6
Rs. 15
This question was previously asked in
UPSC CAPF – 2009
Let O, A, M, P be the costs of one orange, one apple, one mango, and one pineapple respectively.
From the problem statement:
๐Ÿ˜ฏ = 5A
5A = 3M
4M = 8P
3P = 36

From the last equation:
3P = 36 => P = 36 / 3 = 12. So, 1 pineapple costs Rs. 12.

Using the third equation:
4M = 8P => 4M = 8 * 12 = 96 => M = 96 / 4 = 24. So, 1 mango costs Rs. 24.

Using the second equation:
5A = 3M => 5A = 3 * 24 = 72 => A = 72 / 5 = 14.4. So, 1 apple costs Rs. 14.4.

Using the first equation:
๐Ÿ˜ฏ = 5A => ๐Ÿ˜ฏ = 72 => O = 72 / 8 = 9. So, 1 orange costs Rs. 9.

The problem involves a chain of equivalences between the costs of different fruits. The strategy is to start from the known cost (pineapples) and work backwards through the given relationships to find the cost of the desired item (oranges).
This type of problem can also be solved by setting up ratios: O/A = 5/8, A/M = 3/5, M/P = 8/4 = 2/1. To find the ratio of O to P, we can multiply these ratios: (O/A) * (A/M) * (M/P) = O/P. However, since we have the direct cost of P, working backwards is more straightforward.