Question

Some workers have been divided into two groups A and B-depending on their rate of doing work. Three workers from A and six from B take 20 days to complete a job. Eight from A and 4 from B take 10 days to complete it. Find the time taken by one worker from each group to complete it (in days).​

Answer 1

Answer:

A alone will take 90 days , and B alone will take 360 days.

Step-by-step explanation:

solution is attached. thanks for a Good Question.

Answer 2

Given,

1. three workers from A and six from B take ⇒ 20 days for a job
2. eight workers from A and four from B ⇒ 10 days for the same job

To find,

The time taken by one worker of each group to complete the given job

Solution

Let the speed of A be $\frac{1}{A}$ and the speed of B be $\frac{1}{B}$.

Then, the combined speed of 3 workers from A (3A) and 6 workers from B (6B) is

$\frac{3}{A}$ + $\frac{6}{B}$ = $\frac{1}{20}$

⇒ 3B + 6A = $\frac{AB}{20}$

⇒ 60B + 120A = AB (equation x)

Similarly, the combined speed of 8 workers from A (8A) and 4 workers from B (4B) is

$\frac{8}{A}$ + $\frac{4}{B}$ = $\frac{1}{10}$ (equation 1)

⇒ 8B + 4A = $\frac{AB}{10}$

⇒ 80B + 40A = AB (equation y)

We can see from equation x and y that

60B + 120A = 80B + 40A

⇒ 80A = 20B

⇒ A = $\frac{B}{4}$

⇒ $\frac{1}{A}$ =  $\frac{4}{B}$

Substituting in equation 1

$\frac{8}{A}$ + $\frac{1}{A}$ = $\frac{1}{10}$

⇒ $\frac{9}{A}$ = $\frac{1}{10}$

⇒ A = 90

Now , 90 = $\frac{B}{4}$

⇒ B = 360

Hence, time taken by a worker from A is 90 days and by a worker from B is 360 days.