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
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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