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
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,
$\frac{5(k - 40)}{2} +\frac{7(k - 20)}{2} +\frac{17(k - 10)}{9} = 600$
⇒ $45k-1800+63k-1260+34k-340 = 10800$
⇒ $142k = 14200$
∴ $k = \frac{14200}{142} = 100$
Hence, A's share = $\frac{5×(100-40)}{2}$ = Rs. 150
Hence, the correct answer is Rs. 150.
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