Question

working alone Pranav Pratik and Suresh can do a piece of work in 12 days 9 days and 18 days respectively then the work be done if Pranav is assistant by Pratik and Suresh on alternate days​

Answer 1

Answer:

Work is completed in 4.9 days

Step-by-step explanation:

Pranav alone do a piece of work in 12 days

Thus, Pranav's 1 day work $=\frac{1}{12}$

Also, Pratik alone do a piece of work in 9 days

Thus, Pratik's 1 day work $=\frac{1}{9}$

And, Suresh alone do a piece of work in 18 days

Thus, Suresh's 1 day work $=\frac{1}{18}$

Total work is LCM of 12, 9 and 18 $\hspace{0.1cm}=36\hspace{0.1cm}parts$

Pranav's 1 day work $=\frac{36}{12}\hspace{0.1cm}=3\hspace{0.1cm}parts$

Pratik's 1 day work $=\frac{36}{9}\hspace{0.1cm}=4\hspace{0.1cm}parts$

Suresh's 1 day work $=\frac{36}{18}\hspace{0.1cm}=2\hspace{0.1cm}parts$

Given that Pranav is assisted by Pratik and Suresh on alternate days

This means, Pranav work days, while Pratik and Suresh work on alternate days

Thus, work done by Pranav, Pratik and Suresh in 2 days $= (\,3 + 4)\, + (\,3 + 2)\, \hspace{0.1cm}=\hspace{0.1cm}7 + 5 \hspace{0.1cm}=\hspace{0.1cm}13\hspace{0.1cm}parts$

13 parts of work completed in 2 days

Thus, 36 parts of work completed in $\frac{(\,2 \times 36)\,}{13} = 4.9\hspace{0.1cm}days$

Thus, work is completed in 4.9 days

Answer 2

Answer:

Work is completed in 4.9 days

Step-by-step explanation:

Pranav alone do a piece of work in 12 days

Thus, Pranav's 1 day work =\frac{1}{12}=121

Also, Pratik alone do a piece of work in 9 days

Thus, Pratik's 1 day work =\frac{1}{9}=91

And, Suresh alone do a piece of work in 18 days

Thus, Suresh's 1 day work =\frac{1}{18}=181

Total work is LCM of 12, 9 and 18 \hspace{0.1cm}=36\hspace{0.1cm}parts=36parts

Pranav's 1 day work =\frac{36}{12}\hspace{0.1cm}=3\hspace{0.1cm}parts=1236=3parts

Pratik's 1 day work =\frac{36}{9}\hspace{0.1cm}=4\hspace{0.1cm}parts=936=4parts

Suresh's 1 day work =\frac{36}{18}\hspace{0.1cm}=2\hspace{0.1cm}parts=1836=2parts

Given that Pranav is assisted by Pratik and Suresh on alternate days

This means, Pranav work days, while Pratik and Suresh work on alternate days

Thus, work done by Pranav, Pratik and Suresh in 2 days = (\,3 + 4)\, + (\,3 + 2)\, \hspace{0.1cm}=\hspace{0.1cm}7 + 5 \hspace{0.1cm}=\hspace{0.1cm}13\hspace{0.1cm}parts=(3+4)+(3+2)=7+5=13parts

13 parts of work completed in 2 days

Thus, 36 parts of work completed in \frac{(\,2 \times 36)\,}{13} = 4.9\hspace{0.1cm}days13(2×36)=4.9days

Thus, work is completed in 4.9 days