To do a certain work, the ratio of the efficiencies of X and Y is 5:4. Working together, they can complete the same work in 10 days. Y alone starts the work and leaves after 5 days. The remaining work will be completed by X alone in :

Options

A. 14 days
B. 12 days
C. 15 days
D. 10 days

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the efficiencies of X and Y
The ratio of the efficiencies of X and Y is given as 5:4. This means:
- Efficiency of X = 5 units of work per day
- Efficiency of Y = 4 units of work per day

### Step 2: Calculate the total work
When X and Y work together, they complete the work in 10 days.
- The combined efficiency of X and Y = 5 + 4 = 9 units of work per day.
- Therefore, the total work = Combined efficiency × Total days = 9 units/day × 10 days = 90 units of work.

### Step 3: Calculate the work done by Y in 5 days
Y starts the work and works for 5 days.
- Work done by Y in 5 days = Efficiency of Y × Number of days = 4 units/day × 5 days = 20 units of work.

### Step 4: Calculate the remaining work
Now, we need to find out how much work is left after Y has worked for 5 days.
- Remaining work = Total work - Work done by Y = 90 units - 20 units = 70 units of work.

### Step 5: Calculate the time taken by X to complete the remaining work
Now, X will complete the remaining work alone.
- Efficiency of X = 5 units of work per day.
- Time taken by X to complete the remaining work = Remaining work / Efficiency of X = 70 units / 5 units/day = 14 days.

### Final Answer
The remaining work will be completed by X alone in **14 days**.

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