20 persons completed `1/3`rd of the work in 12 days. How many more person are required to finish rest work in next 12 days?

Options

A. 20
B. 12
C. 18
D. 40

Answer

To solve the problem step by step, we will use the information given in the question and apply the concept of work done by a certain number of persons in a given number of days.

### Step 1: Understand the Work Done
We know that 20 persons completed \( \frac{1}{3} \) of the work in 12 days.

### Step 2: Calculate the Total Work
Let’s denote the total work as \( W \). Since \( \frac{1}{3} \) of the work is completed in 12 days, we can express the work done in terms of the total work:
\[ \text{Work done} = \frac{1}{3}W \]

### Step 3: Calculate the Work Rate
The work done by 20 persons in 12 days can be represented as:
\[ \text{Work done} = \text{Number of persons} \times \text{Number of days} \times \text{Work rate} \]
Let’s denote the work rate as \( R \). Therefore:
\[ \frac{1}{3}W = 20 \times 12 \times R \]
\[ \frac{1}{3}W = 240R \]
From this, we can express the total work \( W \):
\[ W = 720R \]

### Step 4: Calculate the Remaining Work
The remaining work is:
\[ \text{Remaining work} = W - \frac{1}{3}W = \frac{2}{3}W \]
Substituting \( W \):
\[ \text{Remaining work} = \frac{2}{3} \times 720R = 480R \]

### Step 5: Determine the Number of Persons Required
We need to finish the remaining work (480R) in the next 12 days. Let \( X \) be the number of persons required to complete this work:
\[ \text{Remaining work} = X \times 12 \times R \]
Setting the two expressions for remaining work equal gives:
\[ 480R = X \times 12 \times R \]
Dividing both sides by \( R \) (assuming \( R \neq 0 \)):
\[ 480 = 12X \]
Now, solving for \( X \):
\[ X = \frac{480}{12} = 40 \]

### Step 6: Calculate the Additional Persons Required
Initially, there were 20 persons. The additional persons required will be:
\[ \text{Additional persons} = X - 20 = 40 - 20 = 20 \]

### Final Answer
Therefore, **20 more persons are required to finish the remaining work in the next 12 days**.

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