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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