Question

Amar baked a cake. John ate 1/6 of the cake. Susan ate 1/5 of what was left. Chan ate 1/4 of what was left after that. Cindy ate 1/3 of what was left after that. Luigi ate 1/2 of what was left after that. How much of the original cake was left?

Answer 1

1/6 of the original cake was left

Explanation:

Let

x ----> complete cake

we know that

1) John ate 1/6 of the cake

so

The remaining cake is equal to

`x-(1)/(6)x=(5)/(6)x`

2) Susan ate 1/5 of what was left

so

`((1)/(5))(5)/(6)x=(1)/(6)x`

The remaining cake is equal to

`(5)/(6)x-(1)/(6)x=(4)/(6)x=(2)/(3)x`

3) Chan ate 1/4 of what was left after that

so

`((1)/(4))(2)/(3)x=(2)/(12)x=(1)/(6)x`

The remaining cake is equal to

`(2)/(3)x-(1)/(6)x=(3)/(6)x=(1)/(2)x`

4) Cindy ate 1/3 of what was left after that

so

`((1)/(3))(1)/(2)x=(1)/(6)x`

The remaining cake is equal to

`(1)/(2)x-(1)/(6)x=(2)/(6)x=(1)/(3)x`

5) Luigi ate 1/2 of what was left after that

so

`((1)/(2))(1)/(3)x=(1)/(6)x`

The remaining cake is equal to

`(1)/(3)x-(1)/(6)x=(1)/(6)x`

therefore

1/6 of the original cake was left