Question : A sum of INR 1,250 has to be distributed among A, B, C, and D. The Total share of B and D is equal to $\frac{14}{11}$ of the total share of A and C. The share of D is half of the share of A. The share of C is 1.2 of the share of A. What are the shares of A, B, C and D respectively?
Option 1: INR 250, INR 575, INR 300, INR 125
Option 2: INR 350, INR 525, INR 300, INR 125
Option 3: INR 250, INR 525, INR 300, INR 125
Option 4: INR 250, INR 575, INR 300, INR 175
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Correct Answer: INR 250, INR 575, INR 300, INR 125
Solution :
Given: A sum of INR 1,250 has to be distributed among A, B, C, and D.
B + D = $\frac{14}{11}$(A + C)
D = $\frac{1}{2}$A and C = 1.2A = $\frac{12}{10}$A = $\frac{6}{5}$A
B + D = $\frac{14}{11}$(A + C)
⇒ 11B + $\frac{11}{2}$A = 14(A + $\frac{6}{5}$A)
⇒ 11B + $\frac{11}{2}$A = 14 × $\frac{11}{5}$A
⇒ 11B = $\frac{154}{5}$A – $\frac{11}{2}$A
⇒ 11B = $\frac{308–55}{10}$A
⇒ 11B = $\frac{253}{10}$A
⇒ B = $\frac{23}{10}$A
According to the question,
A + B + C + D = 1250
⇒ A + $\frac{23}{10}$A + $\frac{6}{5}$A + $\frac{1}{2}$A = 1250
⇒ $\frac{20+46+24+10}{20}$A = 1250
⇒ $\frac{100}{20}$A = 1250
⇒ 5A = 1250
⇒ A = INR 250
The values of B, C, and D are given as,
B = $\frac{23\times 250}{10}$ = INR 575
C = $\frac{6\times 250}{5}$ = INR 300
D = $\frac{250}{2}$ = INR 125
Hence, the correct answer is INR 250, INR 575, INR 300, INR 125.
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