Question

The ratio of efficiency in completing the task of A and B is 2 : 1. If both can complete the work in 10 days, in how many days B alone can complete the work?

Answer 1

Answer:

Step-by-step explanation:

Let us assume the work done is x

A:B=2:1

Using the formula for work done

1/A+1/B=1/A+B

1/2×+1/×=1/10

1/2×+2/2×=1/10

From here x=15

So work done by A is in 15 days and that of B is in 30 days

Answer 2

B will complete work alone in 30 days.

Given ratio is 2 : 1

We need to find the time for work done by B

Let the total work be 1 and A takes time $x$ days and B takes time $y$ days

the efficiency of work is the reciprocal of the number of days.

Therefore,

$\frac{\frac{1}{x}}{\frac{1}{y} }= \frac{2}{1}\\\Rightarrow 2x=y$

Now, according to the question

B complete the work on $2x$ days

So, B will do the work $\frac{1}{2x}$ in a day.

Then B will do in 10 days $\frac{5}{x}$

A complete the work on $x$ days

So, A will do the work $\frac{1}{x}$ in a day.

Then B will do in 10 days $\frac{10}{x}$

Then we get

$\frac{10}{x} + \frac{5}{x} = 1\\\Rightarrow \frac{10+5}{x} = 1\\\Rightarrow \frac{15}{x} = 1\\\Rightarrow x=15$

Therefore, A will complete alone in 15 days and B will complete work alone in 30 days.

To learn more about ratio from the given link

https://brainly.in/question/1798205

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