Sweta and Neha profess to tell their present ages as 25 and 20 years respectively. (Not original age). Ratio of their original ages 5 year ago is 5:4. Sum of ages of both 5 years hence is `(400)/9%` more than the sum of present ages of both professed by them. Find the sum of their present original age

Options

A. A)25
B. B)35
C. C)55
D. D)40

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the given information
Sweta and Neha profess their current ages as 25 and 20 years, respectively. However, these are not their original ages. We need to find their original ages based on the information provided.

### Step 2: Set up the equations based on the original age ratio
We know that the ratio of their original ages 5 years ago was 5:4. Let's denote Sweta's original age 5 years ago as \(5x\) and Neha's original age 5 years ago as \(4x\). Therefore, their current ages can be expressed as:
- Sweta's current age = \(5x + 5\)
- Neha's current age = \(4x + 5\)

### Step 3: Calculate the sum of their professed ages
The sum of their professed ages is:
\[ 25 + 20 = 45 \text{ years} \]

### Step 4: Calculate the sum of their ages 5 years hence
In 5 years, their ages will be:
- Sweta's age = \( (5x + 5) + 5 = 5x + 10 \)
- Neha's age = \( (4x + 5) + 5 = 4x + 10 \)

Thus, the sum of their ages in 5 years will be:
\[ (5x + 10) + (4x + 10) = 9x + 20 \]

### Step 5: Set up the equation based on the percentage increase
It is given that the sum of their ages in 5 years is \( \frac{400}{9}\% \) more than their current professed ages. First, we convert \( \frac{400}{9}\% \) to a fraction:
\[ \frac{400}{9\cdot100} = \frac{4}{90} = \frac{2}{45} \]
This means that the sum of their ages in 5 years is:
\[ \text{Sum in 5 years} = \text{Current sum} + \frac{2}{45} \times \text{Current sum} \]
This can be simplified as:
\[ \text{Sum in 5 years} = 45 + \frac{2}{45} \times 45 = 45 + 2 = 47 \]

### Step 6: Set the equation
Now we equate the two expressions for the sum of their ages in 5 years:
\[ 9x + 20 = 47 \]

### Step 7: Solve for \(x\)
Subtract 20 from both sides:
\[ 9x = 27 \]
Now divide by 9:
\[ x = 3 \]

### Step 8: Calculate the original ages
Now we can find the original ages:
- Sweta's original age = \(5x = 5 \times 3 = 15\)
- Neha's original age = \(4x = 4 \times 3 = 12\)

### Step 9: Find the sum of their original ages
The sum of their original ages is:
\[ 15 + 12 = 27 \text{ years} \]

### Step 10: Conclusion
Thus, the sum of Sweta's and Neha's present original ages is **27 years**.

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