Question

A is twice more efficient than B and he can complete the work 12 days earlier than B. In what time can B complete the work?

Answer 1

Hint: In this question it is given that A is twice more efficient than B and also A can complete the work 12 days earlier than B. So we have to find what time B can complete the work. So to find the solution we first need to consider that in x days B completes the work. So according to the question we can easily write the number of days for A and by solving we will get our required solution i.e, the value of x.

Complete step-by-step solution:
Let us consider B completes the work in x days.
Since, A completes the same work 12 days earlier than B.
Therefore we can write, A completes a work in (x-12) days.
Now since it is given in the question that A is twice more efficient than B, so we can say that A takes half of the time that B.
Therefore, According to the question we can write,
$$\left( x-12\right) =\dfrac{x}{2}$$
$$\Rightarrow 2\left( x-12\right) =x$$ [multiplying both sides by 2]
$$\Rightarrow 2x-2\times 12=x$$
$$\Rightarrow 2x-24=x$$
$$\Rightarrow 2x=x+24$$ [Adding 24 on the both side]
$$\Rightarrow 2x-x=24$$ [Subtracting x from the both side]
$$\Rightarrow x=24$$
Therefore we can say that B completes work in 24 days.

Note: To solve this type of question you need to know that the efficiency of work means, “How much work one person can do in one day”. For example, the efficiency of a person is 2 days. i.e, we can say that he can complete the whole work in 2 days or we can say that he can do half of the total work in 1 day.