The ratio of the present ages of Veer and Zaara 1s 7 : 9 respectively. Four years hence the ratio of their ages will be 15 :19 What is Zaara's present age?

Options

A. 76 years
B. 56 years
C. 72 years
D. 60 years

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Set up the variables based on the given ratio
Let the present age of Veer be \(7x\) and the present age of Zaara be \(9x\), where \(x\) is a common multiplier.

**Hint**: Use the given ratio to express the ages in terms of a variable.

### Step 2: Write the expressions for their ages four years hence
In four years, Veer's age will be \(7x + 4\) and Zaara's age will be \(9x + 4\).

**Hint**: Remember to add 4 years to both ages to find their future ages.

### Step 3: Set up the equation based on the future ratio
According to the problem, the ratio of their ages after four years will be \(15:19\). Therefore, we can set up the equation:
\[ \frac{7x + 4}{9x + 4} = \frac{15}{19} \]

**Hint**: Use the future ages to create a proportion based on the new ratio.

### Step 4: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 19(7x + 4) = 15(9x + 4) \]

**Hint**: Cross-multiplication helps to simplify the equation by removing the fractions.

### Step 5: Expand both sides of the equation
Expanding both sides results in:
\[ 133x + 76 = 135x + 60 \]

**Hint**: Carefully distribute the numbers across the parentheses.

### Step 6: Rearrange the equation to isolate \(x\)
Now, we will rearrange the equation to isolate \(x\):
\[ 133x - 135x = 60 - 76 \]
This simplifies to:
\[ -2x = -16 \]

**Hint**: Move all terms involving \(x\) to one side and constant terms to the other.

### Step 7: Solve for \(x\)
Dividing both sides by -2 gives:
\[ x = 8 \]

**Hint**: When you divide by a negative number, remember to change the sign of the equation.

### Step 8: Calculate Zaara's present age
Now, we can find Zaara's present age:
\[ \text{Zaara's age} = 9x = 9 \times 8 = 72 \]

**Hint**: Substitute the value of \(x\) back into the expression for Zaara's age.

### Final Answer
Zaara's present age is **72 years**.