Question

25 persons can complete a work in 60 days.
They started the work 10 persons left the
work after x days. If the whole work was
Completed in 80 days, thanwhat is the value of x?​

Answer 1

Answer:

30 days.

Step-by-step explanation:

Let us assume that the whole work is W.

So, according to the condition

25 persons need 60 days to complete W work.

⇒25 persons need x days to complete Wx/60 work. ........ (1)

So, by the given condition it is clear that,

(25-10) =15 persons work for (80-x) days to complete the remaining work.

Now,we have,

25 persons need 60 days to complete W work.

⇒15 persons need 60 days to complete (15W/25) work.

⇒15 persons need (80-x) days to complete $\frac{15W}{25}.\frac{(80-x)}{60}$ work.

⇒15 persons need (80-x) days to complete $\frac{W(80-x)}{100}$ work. ......... (2)

Hence, from (1) and (2), we have,

$\frac{Wx}{60}+\frac{W(80-x)}{100}=W$

⇒$\frac{80}{100}-\frac{x}{100}+\frac{x}{60}=1$

⇒$\frac{4}{600}x=\frac{20}{100}$

⇒ x=30 days.

Therefore, after 30 days 10 persons left the work.

(Answer)  

Answer 2

Answer:

30 Days

(A simpler and more practical approach)

Step-by-step explanation:

Let's take total work = (60*25) = 1200 units

So 25 men works 60 days to complete 1200 units.

So 25 men working just 1 day completes 1200/60 units = 25 units

So 1 man completes 1 unit in 1 day.

Now, The question says out of 25 person, 10 leaves the work after x days. Also that the remaining people (15 men) completed the work in 80 days.

It only means that those 15 men worked on all 80 days to complete the work.

So the work completed by 15 men working 80 days = 15*80 = 1200 units.

Remaning work now (1500-1200) = 300 units.

This 300 units was the work done by those 10 men who left after x days.

ie, 10*x = 300

or x = 300/10 = 30 Days