₹ 600 are divided among A, B, C so that ₹ 40 more than 2/5 of A′ s share, ₹ 20 more than 2/7 of B′ s share… · ABC26GN3087

Subject: General Aptitude · Chapter: Ratio and Proportion · Exam: L.I.C.A.A.O. 2007

₹ 600 are divided among $A, B, C$ so that ₹ 40 more than $\frac{2}{5}$ of $A^{\prime}$ s share, ₹ 20 more than $\frac{2}{7}$ of $B^{\prime} s$ share and ₹ 10 more than $\frac{9}{17}$ of $C$ 's share may all be equal. What is $A^{\prime} s$ share?
(a)₹ 150
(b)₹ 170
(c)₹ 200
(d)₹ 280
Answer
Answer (as printed): A
Explanation
$\frac{2}{5} A+40=\frac{2}{7} B+20$ $$\Rightarrow \frac{2}{7} B=\frac{2}{5} A+20 \Rightarrow B=\frac{7}{2}\left(\frac{2}{5} A+20\right)=\frac{7}{5} A+70 .$$ And, $\frac{2}{5} A+40=\frac{9}{17} C+10 \Rightarrow \frac{9}{17} C=\frac{2}{5} A+30$ $$\Rightarrow C=\frac{17}{9}\left(\frac{2}{5} A+30\right)=\frac{34}{45} A+\frac{170}{3} . \begin{aligned} & A+B+C=600 \Rightarrow A+\left(\frac{7}{5} A+70\right)+\left(\frac{34}{45} A+\frac{170}{3}\right)=600 \\ & \Rightarrow \frac{142 A}{45}=600-\frac{380}{3}=\frac{1420}{3} \\ & \Rightarrow A=\frac{1420}{3} \times \frac{45}{142}=150 \end{aligned}$$

Explanation as extracted from the printed page; notation may be imperfect.

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