On her birthday Seema decided to donate some money to children of an orphanage home. If there were 8 children less, everyone would have got ₹10 more. However, if there were 16 children more, everyone would have got ₹10 less. Using the matrix method, find the number of children and the amount distributed by Seema. What values are reflected by Seema’s decision?

Let the number of children = x

and the amount distributed by Seema for one student = ₹y

According to question,

Condition 1:

(x – 8)(y + 10) = xy

⇒ xy + 10x – 8y – 80 = xy

⇒ 10x – 8y = 80

⇒ 5x – 4y = 40 …(i)

Condition 2:

(x + 16)(y – 10) = xy

⇒ xy – 10x + 16y – 160 = xy

⇒ -10x + 16y = 160

⇒ -5x + 8y = 80 …(ii)

It is given that we have to solve this by matrix method.

So, we know that AX = B

and here,

AX = B ⇒ X = A^-1B

Now, we calculate A^-1

So,

⇒ x = 32 and y = 30

Hence, the number of students = 32

Amount given to each student = ₹30

Value reflected by Seema’s decision is that one should help to

needy the person.