Question

A and B can complete a certain task together in 30 days. After A works for 16 days, B is left to finish the remaining work by himself in 44 days. How many days would it take for B to complete the entire task on his own?

• A. 40 days
• B. 50 days
• C. 60 days
• D. 70 days

Answer 1

Answer:

C. 60 days

Let A's one-day work = (a) and B's one-day work = (b).

Since they complete the work together in 30 days,

$a+b=\frac{1}{30}$

A works alone for 16 days, so work done by A:

16a

The remaining work is completed by B alone in 44 days, so the remaining work is:

44b

Hence,

16a + 44b = 1

Substitute $(a=\frac{1}{30}-b):$

$16\left(\frac{1}{30}-b\right)+44b=1$

$\frac{16}{30}+28b=1$
$\frac{8}{15}+28b=1$

$28b=\frac{7}{15}$
$b=\frac{7}{420}=\frac{1}{60}$

Therefore, B alone can complete the entire task in

$\boxed{60\text{ days}}$