The cost of an apple is twice that of a banana and the cost of a banana is 25% less than that of a guava. If the cost of each type of fruit increases by 10%, then the percentage increase in the cost of 4 bananas, 2 apples and 3 guavas is

Options

A. 0.1
B. 0.12
C. 0.16
D. 0.18

Answer

To solve the problem step by step, we will define the costs of the fruits and calculate the percentage increase in their total cost after a 10% increase.

### Step 1: Define the costs of the fruits
Let:
- Cost of a banana = \( B \)
- Cost of an apple = \( 2B \) (since the cost of an apple is twice that of a banana)
- Cost of a guava = \( G \)

According to the problem, the cost of a banana is 25% less than that of a guava. Therefore, we can express this relationship as:
\[ B = G - 0.25G = 0.75G \]

### Step 2: Express the cost of guava in terms of banana
From the equation \( B = 0.75G \), we can express \( G \) in terms of \( B \):
\[ G = \frac{B}{0.75} = \frac{4B}{3} \]

### Step 3: Calculate the total original cost of 4 bananas, 2 apples, and 3 guavas
Now we calculate the total cost before the increase:
- Cost of 4 bananas = \( 4B \)
- Cost of 2 apples = \( 2 \times 2B = 4B \)
- Cost of 3 guavas = \( 3G = 3 \times \frac{4B}{3} = 4B \)

Total original cost:
\[ \text{Total original cost} = 4B + 4B + 4B = 12B \]

### Step 4: Calculate the new costs after a 10% increase
After a 10% increase, the new costs will be:
- New cost of a banana = \( B + 0.1B = 1.1B \)
- New cost of an apple = \( 2B + 0.2B = 2.2B \)
- New cost of a guava = \( G + 0.1G = 1.1G = 1.1 \times \frac{4B}{3} = \frac{4.4B}{3} \)

### Step 5: Calculate the new total cost of 4 bananas, 2 apples, and 3 guavas
Now we calculate the new total cost:
- New cost of 4 bananas = \( 4 \times 1.1B = 4.4B \)
- New cost of 2 apples = \( 2 \times 2.2B = 4.4B \)
- New cost of 3 guavas = \( 3 \times \frac{4.4B}{3} = 4.4B \)

Total new cost:
\[ \text{Total new cost} = 4.4B + 4.4B + 4.4B = 13.2B \]

### Step 6: Calculate the percentage increase in cost
Now we find the percentage increase in cost:
- Increase in cost = New total cost - Original total cost
\[ \text{Increase} = 13.2B - 12B = 1.2B \]

Percentage increase:
\[ \text{Percentage increase} = \left( \frac{\text{Increase}}{\text{Original total cost}} \right) \times 100 \]
\[ \text{Percentage increase} = \left( \frac{1.2B}{12B} \right) \times 100 = 10\% \]

### Final Answer
The percentage increase in the cost of 4 bananas, 2 apples, and 3 guavas is **10%**.