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: $\frac{3}{7}$

Question

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: $\frac{3}{7}$

Team Careers360 · Accepted Answer

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.

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Question : P1 and P2 can do a piece of work together in 14 days, P2 and P3 can do the same work together in 21 days, while P3 and P1 can do it together in 42 days. How much work can all the 3 together do in 12 days?Option 1: 56Option 2: 57Option 3: 67Option 4: 37

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