Question

A certain amount of money is equal divided among some persons. if there were 8 persons more each would have got one rupee less and if 4 persons were less each would have got one rupee extra.find the number of persons

Answer 1

ask if any doubt,thank you

Answer 2

Answer:

The number of persons = 16

Step-by-step explanation:

Let 'p' be the number of people and 'q' be the amount of money each person is getting.

Since the amount is equally distributed, the total amount of money distributed = pq

Case 1:

If there were 8 persons more each would have got one rupee less.

The number of persons, in this case, = p+8

The amount of money each person is getting = q - 1

The total amount distributed in this case = (p+8)(q-1)

Since the amount distributed is the same,

(p+8)(q-1) = pq

pq -p+8q-8 = pq

-p + 8q -8 = 0

p-8q = -8 ---------------(1)

Case 2:

if 4 persons were less each would have got one rupee extra.

The number of persons, in this case, = p-4

The amount of money each person is getting = q + 1

The total amount distributed in this case = (p-4)(q+1)

Since the amount distributed is the same,

(p-4)(q+1) = pq

pq +p-4q-4 = pq

p - 4q -4 = 0

p-4q = 4 ---------------(2)

Subtracting (1) from (2) we get

4q = 12

q = 3

The amount each person will get = 3

Substituting the value of q in equation (1) we get,

p -24 = -8

p = -8+24

p = 16

The number of persons = 16

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