Question

Rahul alone can build a room in 20 days. he start the work and leave it after 5 days. Arjun does the remaining work in 12 days. how long will it take if Arjun did the whole work alone ? how long will it take if Rahul and Arjun work together from the beginning? give answer full concept.

Answer 1

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Answer 2

Arjun alone can build the wall in 16 days and Together both can do the work in $\frac{80}{9}$ days

Solution:

It is given that Rahul alone can build a room in 20 days

In 1 day Rahul will build $\frac{1}{20}$ part of the room.

In 5 days Rahul will build $\frac{1}{20} \times 5=\frac{5}{20}$ part of the room.

Part of the wall remained to be build $=1-\frac{5}{20}$

$=\frac{20-5}{20}$

$=\frac{3}{4}$

Now it is given that Arjun does the remaining work in 12 days which means Arjun does $\frac{3}{4}$ of the work in 12.

Thus Arjun will do the whole work in $12 \times \frac{4}{3}=16 \text { days. }$

Now Rahul can build the wall in 20 days and Arjun can build a wall in 16 days.

Rahul can build 1/20 part of the wall in 1 day and Arjun can build 1/16 part of the wall in 1 day

In 1 day Rahul and Arjun can build $\left(\frac{1}{20}+\frac{1}{16}\right)$ part of the wall

Rahul and Arjun can build $\frac{4+5}{80}=\frac{9}{80}$ part of the wall.

Thus Rahul and Arjun can build the entire wall in $\frac{80}{9}$ days

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