Question

Suresh and ramesh can do a work in 45 days and 40 days respectively. They began the work together, but suresh left after some time, and ramesh finished the remaining work in 23 days. After how many days did suresh leave

Answer 1

Answer:

Thus, Suresh left after 9 days

Step-by-step explanation:

Suresh can complete work in 45 days

Thus, Suresh's 1 day work $=\frac{1}{45}$

Also, Ramesh can complete work in 40 days

Thus, Ramesh's 1 day work $=\frac{1}{40}$

Total work is LCM of 45 and 40 $\hspace{0.1cm}=360\hspace{0.1cm}parts$

Suresh's 1 day work $=\frac{360}{45}\hspace{0.1cm}=8\hspace{0.1cm}parts$

Ramesh's 1 day work $=\frac{360}{40}\hspace{0.1cm}=9\hspace{0.1cm}parts$

(Suresh + Ramesh)'s 1 day work $=\hspace{0.1cm}8 + 9 = \hspace{0.1cm}17\hspace{0.1cm}parts$

Now, Given that Suresh left after some time, and remaining is completed by Ramesh in 23 days

Thus, work completed by Ramesh in 23 days $=\hspace{0.1cm}23 \times 9 = \hspace{0.1cm}207\hspace{0.1cm}parts$

Therefore, Remaining work is completed by both Suresh and Ramesh together.

Now, remaining work $=\hspace{0.1cm}360 - 207 = 153\hspace{0.1cm}parts$

We know,

(Suresh + Ramesh) completes 17 parts in 1 day

(Suresh + Ramesh) completes 153 parts in $\frac{153}{17}\hspace{0.1cm}=\hspace{0.1cm}9\hspace{0.1cm}days$

Thus, Suresh left after 9 days