Question

A works twice as fast as B. If B can complete a work in $12$ days independently, then the number of days in which A and B can together finish the work is:

• A. $4$ days
• B. $6$ days
• C. $8$ days
• D. $18$ days

Answer 1

The correct option is A $4$ days

Ratio of rates of working A and B $=2:1$.

So, the ratio of time taken $=1:2$.

B's 1 day's work $=\frac{1}{12}$

$\therefore$A's 1 day's work $=\frac{1}{6}$

$(A+B{)}^{\prime }s$ 1 day's work $=\frac{1}{6}+\frac{1}{12}=\frac{3}{12}=\frac{1}{4}$

$\therefore (A+B)$ together finish the work in $4$ days.