Question

A is twice as good a workman as b and together they finish a piece of work in 14 days. A alone can finish the work in ?Solution

Answer 1

A alone can finish the work in 21 days if A and B can finish a piece of work in 14 days.

Step-by-step explanation:

It is given that,

A is twice as good a workman as B i.e., A is twice as efficient as B.

Since Efficiency ∝ [1/(Time Taken)]

So, let’s assume that the time taken by A to do a piece of work be “x” days then B will take “2x” days to do the same piece of work.

Therefore,

Work done by A in 1 day = $\frac{1}{x}$

And

Work done by B in 1 day = $\frac{1}{2x}$

Also given that, A & B together can do a piece of work in 14 days.

So, work done by A&B in 1 day = $\frac{1}{14}$

Now, we can write the eq. as,

$\frac{1}{x}$  + $\frac{1}{2x}$  = $\frac{1}{14}$

⇒ [2x + x] / [2x²] = $\frac{1}{14}$  

⇒ 3x / [2x²] = $\frac{1}{14}$

⇒ 3 * 14 = 2x

⇒ x = 3 * 7

⇒ x = 21 days

Thus, A alone can finish the work in 21 days.

---------------------------------------------------------------------------------------

Also View:  

45 men or 60 boys can do a piece of work in 20 days. how many days will 15 men and 20 boys take to complete the work?  

https://brainly.in/question/5181874  

Manish takes 9 days more than his father to do a certain piece of work together they can do the work in 6 days •how many days will Manish take to do that work alone?

https://brainly.in/question/14532722