Question

A and B can do a piece of work in 40 days, B and C in 30 days, and C and A in 24 days. How long does it take if they work on it together?
(a) 14 days
(b) 30 days
(c) 20 days
(d) 18 days

Answer 1

Hint: To solve this question we consider that the total amount of work is 100%. Then, we will find the percentage of work done by A and B is one day, percentage of work done by B and C in one day and percentage of work done by A and C in one day. Then, with this information we will find the percentage of work done in one day when all of them work together and then find the number of days required to complete the work.

Complete step by step solution:
A and B require 40 days to complete 100 % work. So, percentage of work completed by A and B in one day can found out as:
A + B 🡪 $\dfrac{100\%}{40}=2.5\%.......\left( 1 \right)$
B and C required 30 days to complete 100 % work. So, percentage of work completed by B and C in one day can found out as:
 B + C 🡪 $\dfrac{100\%}{30}=3.33\%.......\left( 2 \right)$
C and A required 24 days to complete 100 % work. So, percentage of work completed by C and A in one day can found out as:
 C + A 🡪 $\dfrac{100\%}{24}=4.16\%.......\left( 3 \right)$
Now add (1), (2) and (3) and find the value of A + B + C.
\[\begin{align}
  & \Rightarrow 2A+2B+2C=\left( 2.5+1.33+4.16 \right)\% \\
 & \Rightarrow 2\left( A+B+C \right)=10\% \\
 & \Rightarrow A+B+C=5\% \\
\end{align}\]
So, 5 % of work is completed in one day if A, B and C work together.
Therefore, the number of days to complete the work is $\dfrac{100}{5}=20$.
Therefore, option (c) is the correct option.

Note: Most of the Work-time questions can be solved by finding the work done in unit time. Students can also take the LCM of days instead of 100% to represent the full piece of work.