Question

A person distributes a sum of money among some
beggars. If there had been 6 beggars more, each would
have received a rupee less, but if there had been 4
beggars less each would have received Rs 1 more.
Then the number of beggars are​

Answer 1

Given: A person distributes a sum of money among some  beggars. If there had been 6 beggars more, each would  have received a rupee less, but if there had been 4  beggars less each would have received Rs 1 more.

To find: The number of beggars?

Solution:

• Let number of beggars be x and money distributed be y.

• The total money will be xy.

• According to the question:

• If there had been 6 beggars more, each would  have received a rupee less.

            (x + 6)(y - 1) = xy

            xy - x + 6y - 6 = xy

            6y - x = 6 .......................(i)

• If there had been 4  beggars less each would have received Rs 1 more.

            (x - 4)(y + 1) = xy

            xy + x - 4y - 4 = xy

            x - 4y = 4 .......................(ii)

• Putting value of x from ii in i, we get:

            6y - (4 + 4y) = 6

            6y - 4 - 4y = 6

            2y = 10

            y = 5

• Putting y in i, we get:

            6(5) - x = 6

            30 - 6 = x

            x = 24

Answer:

           So the number of beggars are 24.