Question

$A$ can do a piece of work in $10$ days, $B$ in $15$days. How many days together they will take to complete the same work?

Answer 1

Given,
Number of days A will take to complete the work$=10$
Number of days B will take complete the work$=15$
Step $1$: First find the LCM:
LCM $(10,15)=30$
Step $2$: Find the work by A in a day:
Work can be done by A in a day$=\frac{30}{10}=3units$
Step $3$:Find the work by B in a day:
Work can be done B in a day$=\frac{30}{15}=2units$
Step $4$: Find the work by Both A and B:
A and B work together in a day$=(3+2)units=5units$

Thus, Total number of days required to complete the work by both A and B together $=\frac{30}{5}=6days$