Question : $P_1$ and $P_2$ can do a piece of work together in 14 days, $P_2$ and $P_3$ can do the same work together in 21 days, while $P_3$ and $P_1$ can do it together in 42 days. How much work can all the 3 together do in 12 days?
Option 1: $\frac{5}{6}$
Option 2: $\frac{5}{7}$
Option 3: $\frac{6}{7}$
Option 4: $\frac{3}{7}$
Correct Answer: $\frac{6}{7}$
Solution :
$P_1$ and $P_2$ can do a piece of work together in = 14 days
$P_2$ and $P_3$ can do the same work together in = 21 days
$P_3$ and $P_1$ can do it together in = 42 days
Total work = Time × Efficiency
Total work = LCM(14, 21, 42) = 42 units
Efficiency of $P_1$ and $P_2$ = $\frac{42}{14}$ = 3 units/day
Efficiency of $P_2$ and $P_3$ = $\frac{42}{21}$ = 2 units/day
Efficiency of $P_3$ and $P_1$ = $\frac{42}{42}$ = 1 units/day
Efficiency of $P_1$, $P_2$ and $P_3$ = $\frac{(3 + 2 + 1)}{2}$ = 3 units/day
Work done by all 3 in 12 days = 3 × 12 = 36 units
Part of work done in 12 days = $\frac{36}{42}$ = $\frac{6}{7}$ unit
Hence, the correct answer is $\frac{6}{7}$ unit.
Related Questions
Know More about
Staff Selection Commission Multi Tasking ...
Application | Cutoff | Selection Process | Preparation Tips | Eligibility | Exam Pattern | Admit Card
Get Updates Brochure
Your Staff Selection Commission Multi Tasking Staff Exam brochure has been successfully mailed to your registered email id “”.
Upcoming Exams
Trending Articles around SSC MTS
