Rakesh can complete a job in 6 days, Raman can complete it in x days. If both Ra...

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October 2021 1 15 Report

Rakesh can complete a job in 6 days, Raman can complete it in x days. If both Rakesh and Raman can complete the same job in 4 days, then find the value of x.

Answers & Comments

bhagyashreechowdhury

Given:

Rakesh can complete a job in 6 days

Raman can complete it in x days

Both Rakesh and Raman can complete the same job in 4 days

To find:

The value of x

Solution:

So,

The amount of work done by Rakesh in 1 day = $\frac{1}{6}$

The amount of work done by Raman in 1 day = $\frac{1}{x}$

∴ If both work together, then the amount of work done = $\frac{1}{6} +\frac{1}{x}$

But it is given that,

The amount of work done by both Rakesh and Raman = $\frac{1}{4}$

Therefore, we can form the equation as,

$\frac{1}{6} +\frac{1}{x} = \frac{1}{4}$

⇒ $\frac{x + 6}{6x} = \frac{1}{4}$

⇒ $4[x\:+\:6] = 6x$

⇒ $4x + 24 = 6x$

⇒ $6x - 4x = 24$

⇒ $2x = 24$

⇒ $x = \frac{24}{2}$

⇒ $\bold{x = 12}$

Thus, the values of x is 12 days.

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