10 persons can do a job in X days. If 20 persons with twice the efficiency can do the same job in 5 days, then find the value of X?
A 40 B 15 C 20 D 30

Options

A. B
B. C
C. A
D. D

Answer

To solve the problem, we need to relate the work done by the two groups of people based on their efficiency and the time taken. Let's break it down step by step.

### Step 1: Define the work done by the first group
Let the efficiency of one person be \( E \). Therefore, the total work done by 10 persons in \( X \) days can be expressed as:
\[ \text{Work} = \text{Number of persons} \times \text{Efficiency} \times \text{Time} = 10 \times E \times X \]

### Step 2: Define the work done by the second group
Now, for the second group, we have 20 persons with twice the efficiency. The efficiency of each of these persons is \( 2E \). Therefore, the work done by 20 persons in 5 days can be expressed as:
\[ \text{Work} = \text{Number of persons} \times \text{Efficiency} \times \text{Time} = 20 \times (2E) \times 5 \]

### Step 3: Set the two expressions for work equal
Since both groups are doing the same job, we can set the two expressions for work equal to each other:
\[ 10 \times E \times X = 20 \times (2E) \times 5 \]

### Step 4: Simplify the equation
Now, simplify the right side:
\[ 10 \times E \times X = 20 \times 2E \times 5 \]
\[ 10 \times E \times X = 200E \]

### Step 5: Cancel out the common term
Since \( E \) is common on both sides and \( E \neq 0 \), we can cancel it out:
\[ 10X = 200 \]

### Step 6: Solve for \( X \)
Now, divide both sides by 10:
\[ X = \frac{200}{10} = 20 \]

### Final Answer
The value of \( X \) is 20.