Subject: General Aptitude · Chapter: Ratio and Proportion · Exam: · Marks: · Difficulty:
A person distributed two different amounts among his sons $A, B, C$ and $D$. First amount was distributed in the ratio of $4: 3: 2: 1$ and the second amount was distributed in the ratio of $5: 6: 7: 8$. If the first amount is half of the second amount, then which son will get the maximum amount?
(a)$A$
(b)$B$
(c)$C$
(d)$D$
Answer
Answer (as printed): A
Explanation
Let the first amount be ₹ $x$. Then, second amount $=₹(2 x)$. A'share $=₹\left(\frac{4}{10} \times x+\frac{5}{26} \times 2 x\right)=₹\left(\frac{4 x}{10}+\frac{5 x}{13}\right)=₹\left(\frac{102 x}{130}\right)$. B's share $=₹\left(\frac{3}{10} \times x+\frac{6}{26} \times 2 x\right)=₹\left(\frac{3 x}{10}+\frac{6 x}{13}\right)=₹\left(\frac{99 x}{130}\right)$. C's share $=₹\left(\frac{2}{10} \times x+\frac{7}{26} \times 2 x\right)=₹\left(\frac{2 x}{10}+\frac{7 x}{13}\right)=₹\left(\frac{96 x}{130}\right)$. D's share $=₹\left(\frac{1}{10} \times x+\frac{8}{26} \times 2 x\right)=₹\left(\frac{x}{10}+\frac{8 x}{13}\right)=₹\left(\frac{93 x}{130}\right)$. Clearly, $A$ got the maximum amount.
Explanation as extracted from the printed page; notation may be imperfect.