Rupees 6500 is divided equally among a certain number 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 there be n persons
so each person got share 6500/n
if 15 more persons then
each got 30 less
so each person now got = 6500/ n - 30
which is equal to 6500/ n+ 15
So 6500/n - 30= 6500/ n +15
6500/n - 6500/n +15 = 30
6500 ( 1/n - 1/n +15)= 30
n + 15 - n)/ ( n)( n+15)= 3/650
15/ n ( n+15)= 3/650
15× 650/3 = n(n+15)
5× 650 = n( n+15)
n^2 + 15n -3250= 0
n^2 + 65n -50n -3250 = 0
n( n+65) -50(n+65)= 0
n= 50,-65
So neglect -65
Total no of persons = 50
✌✌Dhruv✌✌✌✌
so each person got share 6500/n
if 15 more persons then
each got 30 less
so each person now got = 6500/ n - 30
which is equal to 6500/ n+ 15
So 6500/n - 30= 6500/ n +15
6500/n - 6500/n +15 = 30
6500 ( 1/n - 1/n +15)= 30
n + 15 - n)/ ( n)( n+15)= 3/650
15/ n ( n+15)= 3/650
15× 650/3 = n(n+15)
5× 650 = n( n+15)
n^2 + 15n -3250= 0
n^2 + 65n -50n -3250 = 0
n( n+65) -50(n+65)= 0
n= 50,-65
So neglect -65
Total no of persons = 50
✌✌Dhruv✌✌✌✌
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