Question

The difference between a number and `45%` of the number is `56`. What is `65%` of the number?

Answer 1

`65%` of the number is `66`

Explanation:

Let the number be `x`, then `45%` of the number is `45/100x`

Difference is `x-45/100x= 55/100x = 56 :. x= (56*100)/55`

`x=1120/11=101 9/11 ~~ 102` ; `65%` of the number is

`1120/11*65/100=(56*13)/11=728/11=66 2/11~~ 66` [Ans]

Answer 2

`65%` of the number is exactly `66 2/11`

Explanation:

Any percentage question can be treated as a direct proportion.

The difference between a number (`100%`) and `45%` of the number is `55%` of the number.

We are told that the difference is `56`

There is another value, `x`, which represents `65%` of the number.

Therefore the ratio between `56 and 55` is the same as the ratio between `x and 65%`

`x/65 = 56/55`

`x = (56xx65)/55`

`x = 66 2/11`

It is interesting to note that we do not need to know the number itself.
(It happens to be `101 9/11`)