Question

A certain number of boys contributed equally to collect ₹240. Had there been 4 boys more to collect the same money, the contribution of each would have decreased by ₹10. Calculate the original number of boys.

Answer 1

Answer:

Original number of boys is $8$.

Step-by-step explanation:

Let the original number of boys be $x$,

and the money they contributed is $y$.

So, $xy=240$.

when four boys added the amount reduces by ten, that is,

$(x+4)(y-10)=240$,

That is all the numbers $x,y,x+4,y-10$ are factors of $240$.

Hence list the factors of $240$ which satisfies both $x,x+4$  and $y,y-10$ are factors of $240$

Factors of $240$ are

$(1,240),(2,120),(3,80),(4,60),(5,18),(6,40),(8,30),(10,24),(12,20).$ and so on

from these we can find that the pairs $(8,30),\(12,20)$

satisfies the properties.

When there are $8$ boys, each contribute $30$, when four boys added

there will be $12$ boys and each contribute $20$

Hence the answer

thank you

Answer 2

Answer:

8 boys

Step-by-step explanation: