A supply of juice lasts for 35 days. If its use is increased by 40% the number of days would the same amount of juice lasts, is :

Options

A. 1. 30 days
B. 2. 27 days
C. 3. 25 days
D. 4. 24 days

Answer

To solve the problem, we need to determine how many days the same amount of juice will last if its usage is increased by 40%.

### Step-by-Step Solution:

1. **Understand the Initial Situation**:
The juice supply lasts for 35 days under normal usage.

2. **Calculate the Daily Usage**:
Let's denote the total amount of juice as \( J \). If the juice lasts for 35 days, the daily usage can be calculated as:
\[ \text{Daily Usage} = \frac{J}{35} \]

3. **Determine the Increased Daily Usage**:
If the usage is increased by 40%, the new daily usage becomes:
\[ \text{New Daily Usage} = \text{Daily Usage} + 0.4 \times \text{Daily Usage} = 1.4 \times \text{Daily Usage} \]
Substituting the daily usage from step 2:
\[ \text{New Daily Usage} = 1.4 \times \frac{J}{35} = \frac{1.4J}{35} \]

4. **Calculate the Number of Days the Juice Will Last with Increased Usage**:
The number of days the juice will last with the new daily usage can be calculated by dividing the total amount of juice \( J \) by the new daily usage:
\[ \text{Days Lasting} = \frac{J}{\text{New Daily Usage}} = \frac{J}{\frac{1.4J}{35}} = \frac{35}{1.4} \]

5. **Perform the Division**:
Now, we calculate \( \frac{35}{1.4} \):
\[ \frac{35}{1.4} = 25 \]

### Final Answer:
The same amount of juice will last for **25 days** if its use is increased by 40%.