Question

10. A sum of money was distributed equally in a class of boys. Had there been 10
boys more, each would have received a rupee less and had there been 15 fewer,
each would have received Rs.3 more. Find the sum of money and the number of
boys.
[4]​

Answer 1

Let the no of boys be x

and each boy got A Rs

then total amount =xa... (1)

10 boys more then each would receive 1 rupee less

boys x+10

each receive A-1

total (X+10)(A-1)......(2)

If 15 boys were less then each would get 3 more Rs

Boys x-15

each receive A+3

Total (X-15)(A+3)....(3)

Total amount is constant

xA=(x+10)(A-1) from (1) and (2)

xA=xA-x+10A-10

10A-10-X=0...(4)

XA=(x-15)(A+3) from (1),(3)

XA=XA+3x-15A-45

X-5A-15=0...(5)

adding (4),(5)

5A-25=0

A=5

and substitution in (4)

10(5)-10=x

40

therefore

no of boys x=40

and money received by each is 5

Total money is 40×5=200