Q. 85.0( 4 Votes )

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?

Answer :

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.


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