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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Updated on: 10-Oct-2022

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