To complete a wall, X takes 20% more time than Y. If together they complete the wall in 30 days, how much time (in days) will Y alone take to complete it?

Options

A. 55
B. 52
C. 44
D. 58

Answer

To solve the problem step by step, we need to find out how much time Y alone will take to complete the wall given that X takes 20% more time than Y and together they complete the wall in 30 days.

### Step 1: Define the time taken by Y
Let the time taken by Y to complete the wall be \( T \) days.

### Step 2: Define the time taken by X
Since X takes 20% more time than Y, the time taken by X will be:
\[ T_X = T + 0.2T = 1.2T \]

### Step 3: Calculate the work done by X and Y
The work done by Y in one day is:
\[ \text{Work done by Y in one day} = \frac{1}{T} \]
The work done by X in one day is:
\[ \text{Work done by X in one day} = \frac{1}{1.2T} = \frac{5}{6T} \]

### Step 4: Calculate the combined work done by X and Y
When X and Y work together, their combined work done in one day is:
\[ \text{Combined work} = \frac{1}{T} + \frac{5}{6T} = \frac{6}{6T} + \frac{5}{6T} = \frac{11}{6T} \]

### Step 5: Set up the equation based on the given information
According to the problem, together they complete the wall in 30 days, which means:
\[ \text{Combined work in 30 days} = 1 \text{ wall} \]
Thus,
\[ 30 \times \frac{11}{6T} = 1 \]

### Step 6: Solve for T
Now, we can solve for \( T \):
\[ \frac{330}{6T} = 1 \]
\[ 330 = 6T \]
\[ T = \frac{330}{6} = 55 \text{ days} \]

### Conclusion
Y alone will take **55 days** to complete the wall.

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