Question

A man spends `10`% of his rupees, then `60`% of the remaining rupees. Given that he has `"Rs."72` left, how many rupees did he start with?

Answer 1

`200`

Explanation:

Suppose the original amount is `x` rupees.

"Percent" means per-cent, i.e. per-hundred, so:

`10%` of `x` is `10/100 x = 0.1 x`

Having spent `10%` of `x` rupees he then has:

`x - 0.1x = (1-0.1)x = 0.9x` rupees

Then:

`60%` of the remaining `0.9x` rupees is:

`60/100 0.9x=0.6*0.9x`

When subtracted from the `0.9x` rupees it leaves:

`0.9x - 0.6*0.9x = (1-0.6)*0.9x = 0.4*0.9x = 0.36x`

We are told that this is `"Rs." 72`, so:

`0.36x = 72`

Divide both sides by `0.36` to find:

`x = 72/0.36 = 200`