Question

Ted can complete a work in 8 days working 12 hours a day. Sid can complete the same work in 16 days working 5 hours a day. If both Ted and Sid work together, working 6 hours a day, in how many days can they complete the work?

• A. 80/11
• B. 61/11
• C. 71/11
• D. 72/11
• E. None of these

Answer 1

The correct option is A

80/11

Ted can complete the work in $(8\times 12)$ hrs = 96 hrs
Sid can complete the work in $(16\times 5)$ hrs = 80 hrs
$\therefore$ Ted's 1 hour's work $=\frac{1}{96}$ and Sid's 1 hour's work $=\frac{1}{80}$
(Ted + Sid)'s 1 hour's work $=(\frac{1}{96}+\frac{1}{80})=\frac{11}{480}$
So, both Ted and Sid will finish the work in $\left(\frac{480}{11}\right)$ hrs
$\therefore$ Number of days 6 hours each $=(\frac{480}{11}\times \frac{1}{6})=\frac{80}{11}$ days = $7\frac{3}{11}$ days