Rs 6500 were divided equally among a certain number of persons. Had there been 15 more persons, each would have got Rs 30 less. Find the original number of persons.

Explanation

Let the original number of persons be x.
Total amount to be divided `=Rs. 6500.`
Share of each `=Rs. (6500)/(x).`
New number persons` =(x+15).`
Now, share of each `=Rs. (6500)/((x+15)).`
`:." "(6500)/(x)-(6500)/((x+15))=30`
`implies" "(1)/(x)-(1)/((x+15))=(30)/(6500)implies((x+15)-x)/(x(x+15))=(3)/(650)`
`implies" "(15)/((x^(2)+15x))=(3)/(650)implies3(x^(2)+15x)=9750`
`implies" "x^(2)+15x=3650impliesx^(2)+15x-3250=0`
`implies" "x^(2)+65x-50x-3250=0impliesx(x+65)-50(x+65)=0`
`implies" "(x+65)(x-50)=0impliesx+65=0" or "x-50=0`
`implies" "x=-65" or "x=50`
`implies" "x=50" "[because" number of persons cannot be negative"]`
Hence, the original number of persons is 50.