A welfare association collected Rs. 202500 as donation from the residents. If each paid as many rupees as there were residents find the number of residents.
Given:
A welfare association collected Rs. 202500 as donation from the residents.
Each paid as many rupees as there were residents.
To do:
We have to find the number of residents.
Solution:
Let the total number of residents be $x$
This implies,
The donation given by each resident $= Rs.\ x$
Therefore,
Total collection $= Rs. x \times x$
$x^{2}=202500$
$x=\sqrt{202500}$
$=\sqrt{2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 5 \times 5 \times 5 \times 5}$ (Prime factorisation of 202500 is $2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 5 \times 5 \times 5 \times 5$)
$=2 \times 3 \times 3 \times 5 \times 5$
$=450$
This implies,
The total number of residents is 450.
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