Question

Ashu takes 12 days to complete the work. Pranav takes 10 days to complete the same work. Ashu, Pranav and Ramu take 5 days to complete the same work. How many days will Ramu take to complete the same work

Answer 1

Given

Work done by Ashu = 12 days

Work done by Pranav = 10 days

Time taken by Ashu, Pranav and Ramu to complete the same work is 5 days.

To find

Time taken by Ramu to complete the same work alone.

Solution

Work done in 1 day by Ashu = $\dfrac{1}{12}$

Work done in 1 day by Pranav = $\dfrac{1}{10}$

Work done by Ramu = x days

Work done in 1 day by Ramu = $\dfrac{1}{x}$

Working together

$\dfrac{1}{12}+\dfrac{1}{10}+\dfrac{1}{x}=\dfrac{1}{5}\\\Rightarrow \dfrac{1}{5}-\dfrac{1}{12}-\dfrac{1}{10}\\\Rightarrow \dfrac{1}{x}=\dfrac{12-5-6}{60}\\\Rightarrow \dfrac{1}{x}=\dfrac{1}{60}\\\Rightarrow x=60\ \text{days}$

Ramu will take 60 days to complete the work alone.