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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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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