Question

Paul and Peter can do a piece of work in 50 days and 55 days. They started to work together but Paul leaves after some days and then Peter completed the remaining work in 22 days. Calculate the number of days after which Paul left the work?

Answer 1

Given:

Paul and Peter can do a piece of work in 50 days and 55 days.

Peter completed the remaining work in 22 days

To find:

The number of days after which Paul left the work

Solution:

In 1 day, the work done by Paul = $\frac{1}{50}$

and

In 1 day, the work done by Peter = $\frac{1}{55}$

So, in 1 day, the work done by Paul and Peter together will be = $[\frac{1}{50}\:+\:\frac{1}{55}]$

Let "x" days be the no. of days after which Paul left the work

It is given to us that after working together for "x" days, Paul leaves and Peter completes the remaining work in 22 days. So, we can form the equation as,

$x[\frac{1}{50}\:+\:\frac{1}{55}] \:+\:\frac{22}{55}\:= 1$

⇒ $x[\frac{11+10}{550}] \:+[\:\frac{22}{55}\:]= 1$

⇒ $x[\frac{21}{550}] \:+[0.4]= 1$

⇒ $x[\frac{21}{550}] \:= 1\:-\:0.4$

⇒ $x[\frac{21}{550}] \:= 0.6$

⇒ $x\:=\:\frac{0.6\:*\:550}{21}$

⇒ $x = 15.71$4

Thus, Paul left the work after 15.714 days.

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Answer 2

The number of days after which Paul left the work is 16

Step-by-step explanation:

The work done by Paul = 1/50

The work done by Peter = 1/55

The number of days after which the Paul leaves be 'x'

Now, the amount of work done by Paul and Peter is given as:

⇒ x[1/50 + 1/55]

The remaining work was completer by Peter in 22 days. Then,

⇒ x[1/50 + 1/55] + 22/55 = 1

x[1/50 + 1/55] = 1 - 22/55

x[21/550] = 33/55

x = 33/55 × 550/21

∴ x = 15.71 ≈ 16 days