Subject: General Aptitude · Chapter: Time and Work · Exam: · Marks: · Difficulty:
P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work ?
(a)$5 \frac{5}{11}$
(b)$5 \frac{6}{11}$
(c)$6 \frac{5}{11}$
(d)$6 \frac{6}{11}$
(e)None of these
Answer
Answer (as printed): A
Explanation
P can complete the work in $(12 \times 8)$ hrs $= 96$ hrs. Q can complete the work in $(8 \times 10)$ hrs $= 80$ hrs. $\therefore$ P's 1 hour's work $= \frac{1}{96}$ and Q's 1 hour's work $= \frac{1}{80}$. (P+Q)'s 1 hour's work $= \left(\frac{1}{96}+\frac{1}{80}\right) = \frac{11}{480}$. So, both P and Q will finish the work in $\frac{480}{11}$ hrs. $\therefore$ Number of days of 8 hours each $= \frac{480}{11} \times \frac{1}{8} = \frac{60}{11} = 5\frac{5}{11}$ days.
Explanation as extracted from the printed page; notation may be imperfect.