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Rupess 6500 where divided equally among a certain no.of persons.Had there been 15 more...

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munsifa | Student, Grade 10 | eNoter

Posted October 27, 2013 at 7:04 PM via web

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Rupess 6500 where divided equally among a certain no.of persons.Had there been 15 more persons each would have got rupees 30 less.Find the original number of persons.

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valentin68 | College Teacher | (Level 3) Associate Educator

Posted October 27, 2013 at 7:25 PM (Answer #1)

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Let the original number of persons be N. Then as the problem is saying

`6500/N =x`  (1)

where `x` is the number of rupees each person got.

Now, if `N ` is increased by 15, `x` is decreased by 30:

`6500/(N+15) =x-30`  (2)

We need to solve (1) and (2) together

`6500/(N+15) =6500/N -30`

`6500*N =6500(N+15) -30N(N+15)`

with the conditions `N!=0 and N!=-15` .

`0 =6500*15 -30N^2-450N`

`2N^2 +30N -6500 =0`

`N^2 +15N -3250 =0`

The solutions are:

`N_1 =50`  and `N_2 =-65`

The second solution does not have physical meaning.

Answer: The original number of persons was 50 (each person got 130 rupee).

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