$₹ 600$ is divided among A, B and C. $₹ 40$ more than $\frac{2}{5}$ th of A’ share, ₹ 20 more than $\frac{2}{7}$ th of B’s share and ₹ 10 more than $\frac{9}{17}$ th of C’s share are all equal. Then A’s share is

According to the question,

A + B + C = 600 .... (i)

and

$\frac{2 \mathrm{~A}}{5}+40=\frac{2 \mathrm{~B}}{7}+20=\frac{9 \mathrm{C}}{17}+10$

$\therefore \frac{2 \mathrm{~A}}{5}+40=\frac{2 \mathrm{~B}}{7}+20=\frac{2 \mathrm{~A}}{5}+20=\frac{2}{7} \mathrm{~B}$

$\therefore \mathrm{B}=\frac{7}{2}\left(\frac{2 \mathrm{~A}}{5}+20\right)=\frac{7 \mathrm{~A}}{5}+70$

Again, $\frac{2 \mathrm{~A}}{5}+40=\frac{9 \mathrm{C}}{17}+10$

$\Rightarrow \frac{9 \mathrm{C}}{17}=\frac{2 \mathrm{~A}}{5}+30$

$\Rightarrow \mathrm{C}=\frac{17}{9}\left(\frac{2 \mathrm{~A}}{5}+30\right)=\frac{34 \mathrm{~A}}{45}+\frac{170}{3}$

$\therefore \mathrm{A}+\frac{7 \mathrm{~A}}{5}+70+\frac{34 \mathrm{~A}}{45}+\frac{170}{3}=600$

$\Rightarrow \mathrm{A}+\frac{7 \mathrm{~A}}{5}+\frac{34 \mathrm{~A}}{45}=600-70-\frac{170}{3}$

$\Rightarrow \frac{45 \mathrm{~A}+63 \mathrm{~A}+34 \mathrm{~A}}{45}=530-\frac{170}{3}$

$\Rightarrow \frac{142 \mathrm{~A}}{45}=\frac{1590-170}{3}=\frac{1420}{3}$

$\Rightarrow \mathrm{A}=\frac{1420}{3} \times \frac{45}{142}=$ Rs. 150