Question

C is four times more efficient as a worker than D, which allows C to complete a work in 45 days less than D. If they work together, they can finish the work in:

• A. 10 days
• B. 12 days
• C. 15 days
• D. 18 days

Answer 1

Answer:

B. 12 days

Let D's efficiency be 1 unit/day.

Then C's efficiency is 4 units/day.

So, if D takes (x) days to finish the work, C takes (\frac{x}{4}) days.

Given:

$x-\frac{x}{4}=45$

$\frac{3x}{4}=45$

x=60

So:

• D takes 60 days

• C takes 15 days

Their combined work rate is:

$\frac{1}{15}+\frac{1}{60}$
$=\frac{4+1}{60}$

$=\frac{5}{60}$

$=\frac{1}{12}$

Hence, together they will complete the work in:

$\boxed{12\text{ days}}$