Question

A, B, and C can complete a certain task in 20, 30, and 60 days, respectively. How many days will it take for A to finish the work if he receives help from B and C every third day?

• A. 15 days
• B. 12 days
• C. 10 days
• D. 9 days

Answer 1

Answer:

A. 15 days

A can complete the work in 20 days.

So, A's 1-day work:

$\frac{1}{20}$

B's 1-day work:

$\frac{1}{30}$

C's 1-day work:

$\frac{1}{60}$

On every third day, A gets help from B and C:

$\frac{1}{20}+\frac{1}{30}+\frac{1}{60}$
$=\frac{3+2+1}{60}$
$=\frac{1}{10}$

Work done in 3 days

• Day 1: A = $(\frac{1}{20})$

• Day 2: A =$(\frac{1}{20})$

• Day 3: A+B+C =$(\frac{1}{10})$

$\frac{1}{20}+\frac{1}{20}+\frac{1}{10}$
$=\frac{1}{5}$

So, in 3 days, they complete $(\frac15)$of the work.

In 15 days:

$5\times\frac15=1$

Answer: 15 days