Question : Rs. 600 is divided among A, B, and C. Rs. 40 more than $\frac{2}{5}$th of A's share, Rs. 20 more than $\frac{2}{7}$th of B's share and Rs. 10 more than $\frac{9}{17}$th C's share are all equal. Then A's share is:
Option 1: Rs. 150
Option 2: Rs. 170
Option 3: Rs. 280
Option 4: Rs. 140
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Correct Answer: Rs. 150
Solution : According to the question, $\frac{2A}{5} + 40 = \frac{2B}{7} + 20 = \frac{9C}{17} + 10 = k$ $\therefore A =\frac{5(k - 40)}{2}, B = \frac{7(k - 20)}{2}, C = \frac{17(k - 10)}{9}$ According to the question, $\frac{5(k - 40)}{2} +\frac{7(k - 20)}{2} +\frac{17(k - 10)}{9}$ = 600 ⇒ $45k - 1800 + 63k - 1260 + 34k - 340 = 10800$ ⇒ $142k = 14200$ $\therefore k = \frac{14200}{142} = 100$ So, A's share = $\frac{5×( 100 - 40)}{2}$ = Rs. 150 Hence, the correct answer is Rs. 150.
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