Question

A works 3 times as fast as B if B completes work in 60 days, then in how many days they will complete the same work together?
A. $12$
B. $15$
C. $18$
D. None of these

Answer 1

Hint: For this question we will first assume the total work and then find out the amount of work done by B in one day. After that, we will multiply it by 3 to find out the amount of work done by A in one day. Finally, we will add them so that we can get the total work done by them together in a single day finally we will find out the total time taken by them to do the complete work.

Complete step-by-step solution:
We will solve this word problem by a unitary method. The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value. This method is used to find the value of a unit from the value of a multiple, and hence the value of a multiple.
Let’s say that the total work is done be $W$.
Now it is given that $B$ completes the work $W$ in $60$ days,
Therefore, in one day the amount of work done will be $=\dfrac{W}{60}$ units.
 Now, it is given in the question that $A$ works $3$ times as fast as $B$ which means $A$ will do$\dfrac{3W}{60}$ units of work in one day.
We will now add both the values obtained that is the work done by $A$ and \[B\] in one day, so the work done by both $A$ and $B$ together in one day will be:
$\left( \dfrac{W}{60}+\dfrac{3W}{60} \right)=\left( \dfrac{4W}{60} \right)=\dfrac{W}{15}$ units of work in one day
Now, if $A$ and $B$ do $\dfrac{W}{15}$ units of work in one day and they need to do a total of $W$ units then we will divide the total work by the work done in one day.
Therefore for $W$ units, they will take: $\dfrac{W}{\left( \dfrac{W}{15} \right)}=\dfrac{W}{W}\times 15=15\text{ days}$ .
Hence, the correct option is B.

Note: Although the unitary method may eventually become a mental algorithm and is easy to learn, it should be shown using carefully written sentences so that its logic is clear to the examiner. The unitary method is universal at can be applied to other types of problems as well.