Question

A and B together can complete a work in 12 days. B and C together can complete the same work in 15 days. C and A together can do it in 20 days. In how many days can A alone complete the job ?

• A. 30 days
• B. 20 days
• C. 50 days
• D. 15 days

Answer 1

Answer:

A. 30 days

Let the one-day work rates of A, B, and C be (a), (b), and (c).

Given:

$a+b=\frac{1}{12}$
$b+c=\frac{1}{15}$
$c+a=\frac{1}{20}$

Add all three equations:

$2(a+b+c)=\frac{1}{12}+\frac{1}{15}+\frac{1}{20}$

Take LCM (=60):

$2(a+b+c)=\frac{5+4+3}{60}=\frac{12}{60}=\frac{1}{5}$
$a+b+c=\frac{1}{10}$

Now find (a):

$a=(a+b+c)-(b+c)$
$a=\frac{1}{10}-\frac{1}{15}$

$=\frac{3-2}{30}=\frac{1}{30}$

So A alone can complete the work in:

$\boxed{30 \text{ days}}$