State whether the given statement is TRUE or FALSE “Rate of doing work is directly proportional to the time taken to do the work.”

Hint: As we know that the rate with which the work is done on a body is defined as the Power. Power is said to be directly proportional to the time taken If with the increase in the time taken to complete the work also increases the consumption of power

Complete step by step answer:
Rate of doing work is termed as Power which is a time based quantity and is related with the speed with which the job is done. Same amount of work can be completed in different amounts of time, one with consuming less amount of time and the other method is by consuming more amount of time and the amount of work done in each case is the same as the same amount of job is identical. But power associated with both the jobs is different.
The power is stated as $P = \dfrac{W}{T}$ .
From the above formula it can be stated easily that the power consumed will be less if the time taken is more hence it is concluded that power consumed by a work is indirectly proportional to the amount of time required to complete that work.

Therefore, the statement stating that the “Rate of doing work is directly proportional to the time taken to do the work” is FALSE.

Note:
we should be careful when stating the equation of power.
Some of us can take power as the product of work done.
AND The time which will introduce a direct relationship between the rate of doing work and time taken to do the work.