Gaurav spends 40% of the amount he received from his father on hostel expenses, 20% on books and stationery and 50% of the remaining on transport. He saves Rs 450 which is half the remaining amount spending on hostel expenses, books etc. and transport.

Solution

Let the money Gaurav inherited be equal to $X$

So, his hostel expenses equal $0.4X$

Expenses on books and stationery is $0.2X$

Remaining amount is $X - 0.4X - 0.2X = 0.4X$

Transport expenses is $50% of 0.4X = 0.2X$

Remaining amount is $0.4X - 0.2X = 0.2X$

He saves $50%$ of it, that is $0.1X$ and it equals $450$.

So, the value of $X$ is $450/0.1 = 4500$

$= 4500$

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