the amount with A is ₹250 and his age is25 years. Amount with B is ₹ 400. if the ratio of the amounts of A and B are in proportion to the ratio of their ages, then find the age of B.

Explanation

To solve the problem step by step, we will use the concept of ratios and proportions.

### Step 1: Understand the given information
- Amount with A (A1) = ₹250
- Age of A (B1) = 25 years
- Amount with B (A2) = ₹400
- Age of B (B2) = ?

### Step 2: Set up the proportion
According to the problem, the ratio of the amounts of A and B is in proportion to the ratio of their ages. This can be expressed as:
\[ \frac{A1}{A2} = \frac{B1}{B2} \]

### Step 3: Substitute the known values
Substituting the known values into the proportion gives us:
\[ \frac{250}{400} = \frac{25}{B2} \]

### Step 4: Cross-multiply to solve for B2
Cross-multiplying gives us:
\[ 250 \times B2 = 400 \times 25 \]

### Step 5: Calculate the right side
Calculating the right side:
\[ 400 \times 25 = 10000 \]
So, we have:
\[ 250 \times B2 = 10000 \]

### Step 6: Solve for B2
Now, divide both sides by 250 to find B2:
\[ B2 = \frac{10000}{250} \]
Calculating this gives:
\[ B2 = 40 \]

### Conclusion
The age of B (B2) is 40 years.

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