Question

There is a mountain with 30 bat caves in a row that contain 340 bats in all. Any 7 caves in a row contain exactly 77 bats. Suppose the first cave has 7 times more bats than the last caves. How many bats in the 29th cave?

Answer 1

The 29th cave has 28 bats.

Explanation:

It is given that any 7 caves in a row contain 77 bats.

So, out of the 30 caves, let us start counting from the second cave till the 29th cave(counting 28 caves).

7 times 4 gives us 28, which has
`77*4=308` bats. We have not counted the first and last cave.

Let the number of bats in the last cave be
`x`, then according to the question:

`7x+x=340-308=32`(First cave has 7 times more bats than the last cave)

Hence,
`x=4`(number of bats in the 30th cave)

Now we shall again count, but this time from the first cave, leaving out the last 2 caves. So the total number of bats in the first 28 caves is 308 and 32 in the last 2 caves.

So, the number of bats in the 29th cave = 32 - 4 = 28