Question : The ratio of monthly incomes of A and B is 4 : 5 respectively. The ratio of monthly savings of A and B is 14 : 19 respectively. If the monthly expenditure of A and B is INR 1200 each, then what is the difference between the monthly incomes of A and B?
Option 1: INR 2000
Option 2: INR 4000
Option 3: INR 1000
Option 4: INR 5000
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Correct Answer: INR 1000
Solution :
Given: The ratio of monthly incomes of A and B is 4: 5 respectively.
The ratio of monthly savings of A and B is 14: 19 respectively.
Let the ratio of monthly incomes of A and B be $4x: 5x$ respectively.
Let the ratio of monthly savings of A and B be $14y: 19y$ respectively.
Income = Saving + Expenditure
According to the question,
$4x=14y+1200$ (equation 1)
$5x=19y+1200$ (equation 2)
Subtract equation (1) from equation (2),
$5x–4x=19y+1200–(14y+1200)$
⇒ $x=19y+1200–14y–1200$
⇒ $x=5y$ (equation 3)
Substitute the above value in the equation (1),
$4\times 5y=14y+1200$
⇒ $20y=14y+1200$
⇒ $6y=1200$
⇒ $y=$ INR 200
From equation (3), $x=5\times 200=$ INR 1000.
The difference between the monthly incomes of A and B $=5x–4x=x=$ INR 1000
Hence, the correct answer is INR 1000.
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