If 15 apples cost as muchas 6 strawberries, 2 strawberries cost as much as 16 bananas, 6 bananas cost as much as 15 potatoes, then whatis the cost of 1 potato if an apple costs ₹ 20?

Options

A. ₹25
B. ₹22.50
C. ₹2.50
D. ₹2.25

Answer

To solve the problem step by step, we will analyze the relationships between the costs of apples, strawberries, bananas, and potatoes.

### Step 1: Establish the relationships between the fruits and vegetables
1. **Given Relationships:**
- 15 apples = 6 strawberries
- 2 strawberries = 16 bananas
- 6 bananas = 15 potatoes

### Step 2: Convert the relationships into ratios
1. **Apples to Strawberries:**
- From 15 apples = 6 strawberries, we can simplify this:
\[ \frac{A}{S} = \frac{6}{15} = \frac{2}{5} \]
- So, 2 apples = 5 strawberries.

2. **Strawberries to Bananas:**
- From 2 strawberries = 16 bananas, we can simplify this:
\[ \frac{S}{B} = \frac{16}{2} = \frac{8}{1} \]
- So, 8 strawberries = 1 banana.

3. **Bananas to Potatoes:**
- From 6 bananas = 15 potatoes, we can simplify this:
\[ \frac{B}{P} = \frac{15}{6} = \frac{5}{2} \]
- So, 5 bananas = 2 potatoes.

### Step 3: Express all items in terms of a single variable
1. **Let’s express everything in terms of apples (A):**
- From \( \frac{A}{S} = \frac{2}{5} \), we can express strawberries in terms of apples:
\[ S = \frac{5}{2}A \]
- From \( \frac{S}{B} = \frac{8}{1} \):
\[ B = \frac{S}{8} = \frac{5}{2 \cdot 8}A = \frac{5}{16}A \]
- From \( \frac{B}{P} = \frac{5}{2} \):
\[ P = \frac{2}{5}B = \frac{2}{5} \cdot \frac{5}{16}A = \frac{2}{16}A = \frac{1}{8}A \]

### Step 4: Find the cost of one potato
1. **Given that the cost of 1 apple (A) is ₹20:**
- We can find the cost of one potato (P):
\[ P = \frac{1}{8}A = \frac{1}{8} \cdot 20 = \frac{20}{8} = 2.5 \]

### Conclusion
The cost of one potato is ₹2.5.