Question

Monu and Sonu can do a work in 25 and 20 days respectively. They started the work together but Monu leaves after few days and Sonu completed the remaining work in 11 days. In how much time (in days) did Monu leave ?

• A. 4
• B. 10
• C. 6
• D. 5

Hint:

Using total units of work makes this even faster:
Let total work $= 100 \text{ units}$ (LCM of $25$ and $20$).
- Monu's rate $= 4 \text{ units/day}$.
- Sonu's rate $= 5 \text{ units/day}$.
Work done by Sonu alone in final 11 days $= 11 \times 5 = 55 \text{ units}$.
Remaining work done together $= 100 - 55 = 45 \text{ units}$.
Since their combined rate is $4 + 5 = 9 \text{ units/day}$, the time they worked together is:
\[ \text{Time} = \frac{45}{9} = 5 \text{ days} \]

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
This problem describes a time and work scenario where one of the workers leaves before the task is finished.
Monu and Sonu start the work together, but after some days, Monu leaves.
Sonu is left to finish the remaining portion of the work alone, taking 11 days.
We need to find the number of days Monu worked before leaving, which is the same as the duration they worked together.

Step 2: Key Formula or Approach:
Let $x$ be the number of days they worked together.
The work done by both together in $x$ days plus the work done by Sonu alone in 11 days must equal the total work ($1$ unit):
\[ x \times (\text{Monu's rate} + \text{Sonu's rate}) + 11 \times (\text{Sonu's rate}) = 1 \]

Step 3: Detailed Explanation:

• Determine the Rates of Work:
- Monu's rate of work $= \frac{1}{25}$ per day.
- Sonu's rate of work $= \frac{1}{20}$ per day.

• Calculate Work Done by Sonu Alone:
Sonu works alone for the final 11 days:
\[ \text{Work done by Sonu alone} = 11 \times \frac{1}{20} = \frac{11}{20} \]

• Calculate the Work Completed Together:
The work done while both were working together is:
\[ \text{Work done together} = 1 - \frac{11}{20} = \frac{9}{20} \]

• Solve for the Number of Days ($x$):
Their combined 1-day rate is:
\[ \frac{1}{25} + \frac{1}{20} = \frac{4 + 5}{100} = \frac{9}{100} \] Since they completed $\frac{9}{20}$ of the work together:
\[ x \times \frac{9}{100} = \frac{9}{20} \] Solve for $x$:
\[ x = \frac{9}{20} \times \frac{100}{9} = 5 \text{ days} \] So, Monu worked for 5 days before leaving the work.

Step 4: Final Answer:
Monu left the work after 5 days.
Therefore, the correct option is (D).