Question

Anuj decided to donate some books for the children living in an orphanage. If there are 8 children less everyone will get 20 rupees more. If there are 7 children more everyone will get 10 rupees less. What is the number of children and how much does each get? What is the total amount distributed? Why Anuj decided to distribute money for books.

Answer 1

Let number of children = c
Let amount to be originally given to each child = n
Then total amount = cn.

When 8 children are absent, then the children left are = (c - 8)
Also each child gets an amount 20 more,
i.e.,each child gets amount = (n + 20)
Hence total amount
= (c - 8)(n + 20) = cn
OR
20c - 8n = 160 ------------(1)

When there are 7 children more, total children = (c + 7)

Also each child gets an amount 10 less,
i.e., each child gets amount = (n - 10)

Hence total amount
= (c + 7)(n - 10) = cn
OR
7n - 10c = 70 -------------(2)

Solving equations (1) and (2) for c and n,
Total no. of children c = 28
Amount per child = 50

Total amount = 28 x 50 = 1400

No conclusion can be drawn from the question as to why Anuj decided to distribute money for books.