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: $\frac{3}{7}$
New: SSC MTS 2024 Application Form OUT; Direct Link
Don't Miss: Month-wise Current Affairs | Upcoming Government Exams
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
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.
Application | Cutoff | Selection Process | Preparation Tips | Eligibility | Exam Pattern | Admit Card
Question : A piece of work can be completed by P and Q together in 24 days, and the same piece of work can be completed by R alone in 60 days. If P and R together can do the same work in 36 days, then find the time taken by Q to complete this piece of work alone.
Question : D1 and D2 can do a piece of work together in 16 days. D2 and D3 can do the same work together in 24 days, while D3 and D1 can do it together in 48 days. In how many days can all 3, working together, do
Question : S alone can do a piece of work in 14 days. T alone can do the same work in 21 days. U alone can do the same work in 28 days. Working together, in how many days will they complete the work?
Question : A can do a piece of work alone in 15 days, while B complete the same piece of work alone in 12 days. If they work on it together for 5 days, then the fraction of the work that will be left is:
Question : Avi alone can do a piece of work in 60 days while Prakash alone can do it in 80 days. In how many days will they finish it together?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile