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?

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Answer 1 · 2016-06-09T17:45:33

$200$

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:

$x = 72/0.36 = 200$

A man spends 1010% of his rupees, then 6060% of the remaining rupees. Given that he has "Rs."72"Rs."72 left, how many rupees did he start with?