3 years ago, the ratio of Maya's and Shikha's age was `5: 9` respectively. After 5 years, this ratio would become `3: 5`. Find present age of Maya?

Options

A. A. 40
B. B. 45
C. C. 43
D. D. 53

Answer

To solve the problem step by step, we will set up equations based on the information given in the question.

### Step 1: Define Variables
Let Maya's present age be \( m \) and Shikha's present age be \( s \).

### Step 2: Set Up the First Equation
According to the problem, 3 years ago, the ratio of Maya's age to Shikha's age was \( 5:9 \). Therefore, we can write the equation:
\[ \frac{m - 3}{s - 3} = \frac{5}{9} \]
Cross-multiplying gives us:
\[ 9(m - 3) = 5(s - 3) \]
Expanding this, we get:
\[ 9m - 27 = 5s - 15 \]
Rearranging terms leads to:
\[ 9m - 5s = 12 \quad \text{(Equation 1)} \]

### Step 3: Set Up the Second Equation
The problem also states that after 5 years, the ratio of their ages will be \( 3:5 \). Thus, we can write the second equation:
\[ \frac{m + 5}{s + 5} = \frac{3}{5} \]
Cross-multiplying gives us:
\[ 5(m + 5) = 3(s + 5) \]
Expanding this, we get:
\[ 5m + 25 = 3s + 15 \]
Rearranging terms leads to:
\[ 5m - 3s = -10 \quad \text{(Equation 2)} \]

### Step 4: Solve the System of Equations
Now we have a system of equations:
1. \( 9m - 5s = 12 \)
2. \( 5m - 3s = -10 \)

We can solve these equations simultaneously. From Equation 1, we can express \( s \) in terms of \( m \):
\[ 5s = 9m - 12 \implies s = \frac{9m - 12}{5} \]

### Step 5: Substitute \( s \) in Equation 2
Now substitute \( s \) into Equation 2:
\[ 5m - 3\left(\frac{9m - 12}{5}\right) = -10 \]
Multiplying through by 5 to eliminate the fraction:
\[ 25m - 3(9m - 12) = -50 \]
Expanding gives:
\[ 25m - 27m + 36 = -50 \]
Combining like terms:
\[ -2m + 36 = -50 \]
Subtracting 36 from both sides:
\[ -2m = -86 \]
Dividing by -2:
\[ m = 43 \]

### Conclusion
Thus, the present age of Maya is \( 43 \) years.