Question: The ratio of weekly incomes of A and B is 9: 7 and the ratio of their expenditures is 4: 3. If each saves Rs. 200 per week, then the sum of their weekly incomes in
Options:
A) Rs. 3600
B) Rs. 3200
C) Rs. 4800
D) Rs. 5600
Show Answer
Answer:
Correct Answer: B
Solution:
- Let As and B’s weekly incomes be Rs. $ 9x $ and Rs. $ 7x $ and their expenditures be Rs. $ 4y $ and Rs. $ 3y $ respectively.
$ \therefore $ $ 9x-4y=200 $
(i)
and $ 7x-3y=200 $
(ii)
$ \Rightarrow $ $ 9x-4y=7x-3y $
$ \Rightarrow $ $ 9x-7x=4y-3y $
$ \Rightarrow $ $ 2x=y $
(iii)
From Eq. (i),
$ 9x-4y=200 $
$ \Rightarrow $ $ 9x-8x=200 $
$ \therefore $ $ x=200 $
$ \therefore $ Sum of their weekly incomes $ =16x=16\times 200 $
$ =Rs\text{.}3200 $
Alternate Method
Let A’s income $ =Rs\text{.}9x $
B’s income $ =Rs\text{.}7x $
According to the question,
$ \frac{9x-200}{7x-200}=\frac{4}{3} $
$ \Rightarrow $ $ 27x-600=28x-800 $
$ \Rightarrow $ $ x=200 $
A’s income $ =9\times 200=Rs\text{. 1800} $
and B’s income $ =7\times 200=Rs\text{. 1400} $
Sum $ =1400+1800=Rs\text{. 3200} $
BETA
