X and Y together can do a piece of work in 10 days .X is 40 % more efficient than Y.X alone will completes 35 % of the same work in :

Options

A. 6 days
B. 8 days
C. 9 days
D. 5 days

Answer

To solve the problem step by step, we can follow the below approach:

### Step 1: Determine the efficiency of X and Y
Given that X is 40% more efficient than Y, we can express their efficiencies in terms of Y's efficiency.

Let the efficiency of Y be \( E_Y \).
Then, the efficiency of X, \( E_X \), can be expressed as:
\[ E_X = E_Y + 0.4 \cdot E_Y = 1.4 \cdot E_Y \]

### Step 2: Calculate the combined efficiency of X and Y
When X and Y work together, their combined efficiency is:
\[ E_{X+Y} = E_X + E_Y = 1.4E_Y + E_Y = 2.4E_Y \]

### Step 3: Calculate the total work done by X and Y together in 10 days
We know that X and Y together can complete the work in 10 days. Therefore, the total work \( W \) can be calculated as:
\[ W = E_{X+Y} \times \text{Time} = 2.4E_Y \times 10 = 24E_Y \]

### Step 4: Calculate the work done by X alone
Now, we need to find out how much work X can complete alone. We know that X will complete 35% of the total work \( W \):
\[ \text{Work done by X} = 0.35W = 0.35 \times 24E_Y = 8.4E_Y \]

### Step 5: Calculate the time taken by X to complete 35% of the work
To find the time \( T \) taken by X to complete this work, we can use the formula:
\[ T = \frac{\text{Work}}{\text{Efficiency}} = \frac{8.4E_Y}{1.4E_Y} \]
The \( E_Y \) cancels out:
\[ T = \frac{8.4}{1.4} = 6 \text{ days} \]

### Final Answer
Thus, X alone will complete 35% of the same work in **6 days**.

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