Question

A alone can do a piece of work in 10 days and B alone can do the same work in 15 days. They started working together. After two days, both of them left the work. If C alone can complete the remaining work in 5 days, then in how many days can C alone complete the work?

• A. 8.5 days
• B. 7.5 days
• C. 7 days
• D. 8 days
• E. None of these

Answer 1

The correct option is B 7.5 days

Total work = L.C.M of 10 and 15 = 30 units

$A^{\prime }s1-daywork=\frac{30}{10}=3units$

$B^{\prime }s1-daywork=\frac{30}{15}=2units$

(A + B)’s 1-day work = 3 + 2 = 5 units

Now (A + B)’s 2-day work = $2\times 5$=10 units

Remaining work = 30 – 10 = 20 units

20 units of work done by C in 5 days

30 units of work done by C in $\frac{5}{20}\times 30=7.5days.$

So, C alone can complete the whole work in 7.5 days