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. 25days
B. 30days
C. 24days
D. 27days

Answer

To solve the problem step by step, we will break down the information given and perform the necessary calculations.

### Step 1: Understand the initial consumption
The juice supply lasts for 35 days. This means that the total consumption of juice can be represented as 1 unit of juice lasting for 35 days.

**Hint:** Think of the total amount of juice as a single unit that is consumed over a period of time.

### Step 2: Calculate the daily consumption
If the juice lasts for 35 days, the daily consumption can be calculated as:
\[ \text{Daily Consumption} = \frac{1 \text{ unit}}{35 \text{ days}} = \frac{1}{35} \text{ units per day} \]

**Hint:** Daily consumption is the total amount divided by the number of days it lasts.

### Step 3: Increase the consumption by 40%
If the daily consumption is increased by 40%, we need to calculate the new daily consumption. The new consumption will be:
\[ \text{New Daily Consumption} = \text{Original Daily Consumption} + 40\% \text{ of Original Daily Consumption} \]
This can be expressed mathematically as:
\[ \text{New Daily Consumption} = \frac{1}{35} + 0.4 \times \frac{1}{35} \]
Calculating this gives:
\[ \text{New Daily Consumption} = \frac{1}{35} + \frac{0.4}{35} = \frac{1 + 0.4}{35} = \frac{1.4}{35} \]

**Hint:** To find a percentage increase, multiply the original value by the percentage (in decimal form) and add it to the original value.

### Step 4: Simplify the new daily consumption
We can simplify the new daily consumption:
\[ \text{New Daily Consumption} = \frac{1.4}{35} = \frac{14}{350} = \frac{2}{50} = \frac{1}{25} \text{ units per day} \]

**Hint:** Simplifying fractions can help make calculations clearer.

### Step 5: Calculate how many days the juice will last with the new consumption
Now that we have the new daily consumption, we can find out how many days the same amount of juice will last:
\[ \text{Days Juice Lasts} = \frac{1 \text{ unit}}{\text{New Daily Consumption}} = \frac{1}{\frac{1}{25}} = 25 \text{ days} \]

**Hint:** To find out how long something will last, divide the total amount by the new rate of consumption.

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

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