Question

Suppose a person A can finish a job in 12 days. He worked three days when a person B joins him to help. Suppose the person B can finish the same job in 15 days. How long will they take to finish the job.

Answer 1

Given:

Person A can finish a job in 12 days

He worked three days when a person B joins him to help

Person B can finish the same job in 15 days

To find:

How long will they take to finish the job?

Solution:

Let's assume,

"x" → represents the no. of days that A & B will take to finish the job

Also, the total amount of job done is represented as → "1".

A can do a job in 12 days

So, in 1 day, A will do = $\frac{1}{12}$ of the job

∴ In 3 days, A will do =  $\frac{3}{12}$ of the job = $\frac{1}{4}$ of the job

B can do a job in 15 days

So, in 1 day, B will do = $\frac{1}{15}$ of the job

Now, according to the question, we can form an equation as:

[Work done by A in 3 days] + [Work done by A & B in x days] = 1

$\implies [\frac{1}{4} ] + x[\frac{1}{12} + \frac{1}{15} ] = 1$

$\implies [\frac{1}{4} ] + x[\frac{5+4}{60} ] = 1$

$\implies [\frac{1}{4} ] + x[\frac{9}{60} ] = 1$

$\implies \frac{9x}{60} = 1 - \frac{1}{4}$

$\implies \frac{9x}{60} = \frac{4-1}{4}$

$\implies \frac{9x}{60} = \frac{3}{4}$

$\implies x = \frac{3\times 60}{4\times 9}$

$\implies x = \frac{180}{36}$

$\implies\bold{x = 5\:days}$

Thus, A & B will take 5 days to finish the job.

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