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Question

The annual income of two persons are in the ratio 9 : 7 and their expenses are in the ratio 4 : 3. If each of them saves Rs. 2000 per year, then their annual incomes are

(1) Rs.18000 and Rs.14000

(2) Rs.27000 and Rs. 21000

(3) Rs. 36000 and Rs. 28000

(4) Rs. 45000 and Rs. 35000


Solution

9X-4Y=2000               (1)
7X-3Y=2000               (2)

SUBSTITUTION METHOD 
9X-4Y=2000 
X=2000+4Y/9    (apply X in equation (2) )

7X-3Y=2000
7(2000+4Y/9)-3Y=2000

14000+28Y-27Y=18000

Y=18000-14000= 4000    therefore, (Y=4000)

substitute Y in equation (1)
9X-4y=2000
9X-4(4000)= 2000
9X-16000=2000
9X=2000+16000= 18000
X=18000/9= 2000         therefore, (X=2000)


MONTHLY INCOME -
first person- 9(2000) = 18000
second person - 7(2000) = 14000


So first option is correct

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