While working 5 hours a day, X alone can cut 15 trees in 9 days. In how many days X can cut 40 trees working 8 hours a day?

Options

A. 15
B. 18
C. 14
D. 17

Answer

To solve the problem step by step, we will use the information given and apply the formula for work done.

### Step 1: Calculate the total work done by X in terms of trees cut
X can cut 15 trees in 9 days while working 5 hours a day.

Total hours worked by X = Number of days × Hours worked per day
= 9 days × 5 hours/day = 45 hours

### Step 2: Calculate the rate of work of X
The rate of work (trees per hour) can be calculated as:
Rate of work = Total trees cut / Total hours worked
= 15 trees / 45 hours = 1/3 trees per hour

### Step 3: Calculate the total hours needed to cut 40 trees
Now, we need to find out how many hours it will take X to cut 40 trees at the same rate:
Total hours needed = Total trees to cut / Rate of work
= 40 trees / (1/3 trees per hour) = 40 × 3 = 120 hours

### Step 4: Calculate the number of days needed when working 8 hours a day
Now, if X works 8 hours a day, we can find the number of days (Y) required to complete the work:
Number of days = Total hours needed / Hours worked per day
= 120 hours / 8 hours/day = 15 days

Thus, X can cut 40 trees working 8 hours a day in **15 days**.

### Final Answer:
X can cut 40 trees in **15 days** working 8 hours a day.

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