Question : A and B together can do a certain work in $x$ days. Working alone, A and B can do the same work in ($x$ + 8) and ($x$ + 18) days, respectively. A and B together will complete $\frac{5}{6}$th of the same work in:
Option 1: 12 days
Option 2: 8 days
Option 3: 10 days
Option 4: 9 days
Correct Answer: 10 days
Solution :
According to the question,
One day work of A = $\frac{1}{x + 8}$ work per day
One day work of B = $\frac{1}{x + 18}$ work per day
One day work of (A + B) = $\frac{1}{x}$
⇒ $\frac{1}{x + 8 }$ + $\frac{1}{x + 18}$ = $\frac{1}{x}$
⇒ $\frac{x + 18 + x + 8}{(x + 18)(x + 8)}$ = $\frac{1}{x}$
⇒ $\frac{2x + 26}{(x + 18)(x + 8)}$ = $\frac{1}{x}$
⇒ $2x^{2} + 26x = x^{2} + 26x + 144$
⇒ $x^{2} − 144 = 0$
⇒ $x = 12$ days
$\therefore$ A and B together can finish $\frac{5}{6}$th of the work in $12 × \frac{5}{6}$ = 10
Hence, the correct answer is 10 days.
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