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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