CBSE Class 12 · 2016 · MatricesLong Answer

The monthly incomes of Aryan and Babban are in the ratio

3 : 4

and their monthly expenditures are in the ratio

5 : 7

. If each saves Rs. 15,000 per month, find their monthly incomes using the matrix method. This problem reflects which value?

Answer: Aryan Rs. 90,000 and Babban Rs. 1,20,000

Solution

Let incomes be

3 x

and

4 x

, expenditures

5 y

and

7 y

. Since saving

=

income

-

expenditure

= 15000

for each:

3 x - 5 y = 15000, 4 x - 7 y = 15000.

In matrix form

[34 - 5 - 7] [x y] = [1500015000]

. Solving gives

x = 30000

(and

y = 15000

).
Incomes: Aryan

= 3 x = Rs. 90, 000

, Babban

= 4 x = Rs. 1, 20, 000

.
Value reflected: the importance of saving / thrift (Aryan saves as much as Babban despite earning less).

CBSE Class 12 Board · 2016 · Subjective