Question : A's income is INR 140 more than B's income, and C's income is INR 80 more than D's. If the ratio of A's and C's incomes is 2 : 3 and the ratio of B's and D's incomes is 1 : 2, then the incomes of A, B, C, and D are, respectively:
Option 1: INR 260, INR 120, INR 320, and, INR 240
Option 2: INR 300, INR 160, INR 600, and INR 520
Option 3: INR 400, INR 260, INR 600, and INR 520
Option 4: INR 320, INR 180, INR 480, and INR 360
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Correct Answer: INR 400, INR 260, INR 600, and INR 520
Solution : Given: A's income is INR 140 more than B's C's income is INR 80 more than D's Income of A: C = 2 : 3 Income of B: D = 1 : 2 Let the income of A and C be $2x$ and $3x$, respectively. Then B's income = $2x-140$. D's income = $3x-80$ According to the question, $\frac{2x-140}{3x-80}=\frac{1}{2}$ $⇒4x-280=3x-80$ $⇒4x-3x=280-80$ $⇒x=200$ $\therefore$ A's income = 2 × 200 = 400 B's income = 2 × 200 – 140 = 260 C's income = 3 × 200 = 600 D's income = 3 × 200 – 80 = 520 Hence, the correct answer is INR 400, INR 260, INR 600, and INR 520.
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