₹ 600 is divided among A, B and C. If frac{2} | vedclass

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(A) Let the shares of $A, B,$ and $C$ be $a, b,$ and $c$ respectively.Given that $a + b + c = 600$.According to the problem:$\frac{2}{5}a + 40 = \frac

Vedclass · Accepted Answer

$150$

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(A) Let the shares of $A, B,$ and $C$ be $a, b,$ and $c$ respectively.Given that $a + b + c = 600$.According to the problem:$\frac{2}{5}a + 40 = \frac{2}{7}b + 20 = \frac{9}{17}c + 10 = k$ (let this be $k$).Then,$\frac{2}{5}a = k - 40 \implies a = \frac{5}{2}(k - 40) = 2.5k - 100$.$\frac{2}{7}b = k - 20 \implies b = \frac{7}{2}(k - 20) = 3.5k - 70$.$\frac{9}{17}c = k - 10 \implies c = \frac{17}{9}(k - 10) = \frac{17}{9}k - \frac{170}{9}$.Substituting these into $a + b + c = 600$:$(2.5k - 100) + (3.5k - 70) + (\frac{17}{9}k - \frac{170}{9}) = 600$.$6k - 170 + \frac{17}{9}k - \frac{170}{9} = 600$.$\frac{54k + 17k}{9} = 770 + \frac{170}{9}$.$\frac{71k}{9} = \frac{6930 + 170}{9} = \frac{7100}{9}$.$71k = 7100 \implies k = 100$.Now,$A$'s share $a = 2.5(100) - 100 = 250 - 100 = 150$.

₹ $600$ is divided among $A, B$ and $C$. If $\frac{2}{5}$ of $A$'s share plus ₹ $40$,$\frac{2}{7}$ of $B$'s share plus ₹ $20$,and $\frac{9}{17}$ of $C$'s share plus ₹ $10$ are all equal,then what is $A$'s share in ₹?

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