Question

A can finish a work in 18 days and B can do the same work in 15 days . B worked for 10 days and left the job . In how many days A alone can finish the remaining work?
A. 5
B. $5\dfrac{1}{2}$
C. 6
D. 8

Answer 1

Hint: In this particular type of question we have to find the efficiency of A and B using the LCM time taken by both of them to complete the work. Then we need to calculate the work needed to be done and use the efficiency to find the desired result.

Complete step-by-step answer:
A can finish a work in 18 days and B can do the same work in 15 days.
The LCM of 18, and 15 is:
18 =$3 \times 3 \times 2$
15 = $5 \times 3$
LCM = $3 \times 3 \times 2 \times 5$ = 90 Units

Now efficiency of A is $\dfrac{{90}}{{18}}$= 5 units per day.
The efficiency of B is $\dfrac{{90}}{{15}}$= 6 units per day.
B work for 10 days, thus.
10$ \times $6 = 60 units
That means the remaining work is 90 - 60 = 30 units.

Now time taken by A to complete the remaining work =
=$\dfrac{{{\text{work left}}}}{{{\text{efficiency}}}} = \dfrac{{30}}{5} = 6 days$

Note: Remember to recall the procedure of finding efficiency of an individual using the time taken by him to complete the work . Note that the time taken to complete the work increases when the number of people decreases or the efficiency decreases . Always remember that efficiency of a person is the amount of work done by him in a single day .