The ratio between the ages of Rati and Madhuri is 4:5 and the ratio between the ages of Madhuri and Kajri is 5:6 . If the sum of their ages is 60 years , what is the age of Kajri ?

Options

A. 20 years
B. 16 years
C. 28 years
D. 24 years

Answer

To find the age of Kajri, we will follow these steps:

### Step 1: Define the ratios
Let the ages of Rati, Madhuri, and Kajri be represented as:
- Rati's age = 4x
- Madhuri's age = 5x
- Kajri's age = 6y

### Step 2: Establish relationships
From the problem, we know:
1. The ratio of Rati's age to Madhuri's age is 4:5, which we have represented as \( Rati = 4x \) and \( Madhuri = 5x \).
2. The ratio of Madhuri's age to Kajri's age is 5:6, which can be expressed as \( Madhuri = 5y \) and \( Kajri = 6y \).

### Step 3: Relate the two ratios
Since Madhuri's age is common in both ratios, we can equate the two expressions for Madhuri:
\[ 5x = 5y \]
This implies that \( x = y \).

### Step 4: Substitute and express ages in terms of x
Now we can express all ages in terms of x:
- Rati's age = 4x
- Madhuri's age = 5x
- Kajri's age = 6x

### Step 5: Set up the equation for the sum of their ages
According to the problem, the sum of their ages is 60 years:
\[ 4x + 5x + 6x = 60 \]

### Step 6: Simplify the equation
Combine the terms:
\[ 15x = 60 \]

### Step 7: Solve for x
To find x, divide both sides by 15:
\[ x = \frac{60}{15} = 4 \]

### Step 8: Calculate Kajri's age
Now that we have the value of x, we can find Kajri's age:
\[ Kajri's \, age = 6x = 6 \times 4 = 24 \]

### Conclusion
Thus, Kajri's age is **24 years**.

---