Question : A is twice as good a workman as B, and together they finish a piece of work in 13 days. In how many days will A alone finish the work?
Option 1: $41$
Option 2: $39$
Option 3: $19 \frac{1}{2}$
Option 4: $9 \frac{1}{4}$
Correct Answer: $19 \frac{1}{2}$
Solution : Let the amount of work A can do in one day as $a$ and the amount of work B can do in one day as $b$. Given that A is twice as good a workman as B. $⇒a = 2b$ Also, given that A and B together can finish the work in 13 days. $⇒(a + b) \times 13 = 1$ (assuming the total work to be 1 unit). Substituting $a = 2b$ into the equation, $⇒(2b + b) \times 13 = 1$ $⇒3b \times 13 = 1$ $⇒b = \frac{1}{3 \times 13} = \frac{1}{39}$ Substituting $b = \frac{1}{39}$ into $a = 2b$, $⇒a = 2 \times \frac{1}{39} = \frac{2}{39}$ So, A can do $\frac{2}{39}$ of the work in one day. Therefore, A will take $\frac{1}{\frac{2}{39}} = \frac{39}{2} = 19 \frac{1}{2}$ days to finish the work alone. Hence, the correct answer is $19 \frac{1}{2}$.
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