Question

25. A and B individually can do a work in 8 hours
and 12 hours respectively. A worked first for 2
hours and then left. How long will B take to
finish the remaining part of the work ?​

Answer 1

Answer:

B will take 9 hours to complete the remaining work.

Step-by-step explanation:

Let the work to be done be denoted by W

Time taken by A to complete the work = 8 hours

Rate at which A does the work = $\dfrac{W}{8}$

Time taken by B to complete the work = 12 hours

Rate at which B does the work = $\dfrac{W}{12}$

Work done by A in the 2 hours = $\dfrac{W}{8}\times 2$  = $\dfrac{W}{4}$

Work to be completed by B after A leaves = $W-\dfrac{W}{4}$  =  $\dfrac{3W}{4}$

Rate of work done = $\frac{work}{time}$

∴ Time taken = $\frac{work}{rate}$

                      = $\dfrac{3W}{4}\div \dfrac{W}{12}$

                      = 3 × 3

                      = 9 hours

Hence B will take 9 hours to complete the remaining work.