35 persons are engaged to complete a work in 60 days. After 32 days it is observed that only (2/5)th part of the work has been done. The number of persons to be engaged to complete the remaining work in the said period is

Options

A. 20
B. 35
C. 30
D. 25

Answer

To solve the problem step by step, let's break it down:

### Step 1: Determine the total amount of work
We know that 35 persons are engaged to complete the work in 60 days. Therefore, the total work can be expressed in terms of "man-days".

Total work = Number of persons × Number of days
Total work = 35 persons × 60 days = 2100 man-days

**Hint:** Remember that "man-days" is a way to express the total work done by a certain number of people over a certain number of days.

### Step 2: Calculate the work done in 32 days
After 32 days, it is observed that \( \frac{2}{5} \) of the work has been completed.

Work done = \( \frac{2}{5} \) of Total work
Work done = \( \frac{2}{5} \) × 2100 man-days = 840 man-days

**Hint:** To find the work done, multiply the fraction of work completed by the total work.

### Step 3: Calculate the remaining work
To find the remaining work, we subtract the work done from the total work.

Remaining work = Total work - Work done
Remaining work = 2100 man-days - 840 man-days = 1260 man-days

**Hint:** The remaining work is simply the total work minus the work that has already been completed.

### Step 4: Determine the remaining time
The total time given for the work is 60 days, and 32 days have already passed.

Remaining time = Total time - Time passed
Remaining time = 60 days - 32 days = 28 days

**Hint:** Subtract the time already spent from the total time to find out how much time is left.

### Step 5: Calculate the number of persons needed to complete the remaining work
Now, we need to find out how many persons are required to complete the remaining work in the remaining time.

Let \( x \) be the number of persons required.

We can set up the equation:
Remaining work = Number of persons × Remaining time
1260 man-days = \( x \) persons × 28 days

Now, solving for \( x \):
\( x = \frac{1260 \text{ man-days}}{28 \text{ days}} \)
\( x = 45 \) persons

**Hint:** To find the number of persons needed, divide the remaining work by the remaining time.

### Step 6: Calculate the additional persons needed
Since there are already 35 persons working, we need to find out how many additional persons are required.

Additional persons needed = Total persons required - Persons already working
Additional persons needed = 45 persons - 35 persons = 10 persons

**Hint:** To find the additional number of persons required, subtract the current number of workers from the total number needed.

### Final Answer
The number of persons to be engaged to complete the remaining work in the said period is **10 persons**.