Question : A sum of INR 46, 800 is divided among A, B, C, and D in such a way that the ratio of the combined share of A and D to the combined share of B and C is 8: 5. The ratio of the share of B to that of C is 5 : 4. A receives INR 18,400. If $x$ is the difference between the shares of A and B and $y$ is the difference between the shares of C and D, then what is the value of ($x$ – $y$) (in INR)?
Option 1: 7000
Option 2: 6000
Option 3: 6500
Option 4: 5000
Correct Answer: 6000
Solution :
According to the question
(A + D) : (B + C) = 8 : 5
Share of (A + D) = $\frac{8}{13}$ × 46800 = 28800
and, share of (B + C) = $\frac{5}{13}$ × 46800 = 18000
Also, B : C = 5 : 4
Share of B = $\frac{5}{9}$ × 18000 = 10000
and, Share of C = $\frac{4}{9}$ × 18000 = 8000
Share of A = 18,400
Then,
Share of D = 28800 - 18400 = 10400
Now,
$x$ = A – B = 10400 – 8000 = 8400
and $y$ = D – C = 10400 - 8000 = 2400
So, $x -y$ = 8400 – 2400 = INR 6000
Hence, the correct answer is 6000.
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