Rani's weight is 25% that of Meena's and 40% that of Tara's. What percentage of Tara's weight is equal to Meena's weight?

Options

A. 1.6
B. 1.4
C. 1.2
D. 1

Answer

To solve the problem step by step, we will denote the weights of Rani, Meena, and Tara using variables and percentages.

### Step 1: Define Variables
Let Meena's weight be \( M \). According to the problem:
- Rani's weight is 25% of Meena's weight.
- Rani's weight is also 40% of Tara's weight.

We can express Rani's weight in terms of Meena's weight:
\[ R = 0.25M \]

### Step 2: Express Rani's Weight in Terms of Tara's Weight
Let Tara's weight be \( T \). Since Rani's weight is also 40% of Tara's weight, we can express this as:
\[ R = 0.40T \]

### Step 3: Set the Two Expressions for Rani's Weight Equal
Now we have two expressions for Rani's weight:
1. \( R = 0.25M \)
2. \( R = 0.40T \)

Setting them equal gives us:
\[ 0.25M = 0.40T \]

### Step 4: Solve for Meena's Weight in Terms of Tara's Weight
To find the relationship between Meena's weight and Tara's weight, we can rearrange the equation:
\[ M = \frac{0.40T}{0.25} \]
\[ M = \frac{0.40}{0.25}T \]
\[ M = 1.6T \]

### Step 5: Find the Percentage of Tara's Weight that is Meena's Weight
To find what percentage of Tara's weight is equal to Meena's weight, we can express this as:
\[ \text{Percentage} = \left( \frac{M}{T} \right) \times 100 \]

Substituting \( M = 1.6T \):
\[ \text{Percentage} = \left( \frac{1.6T}{T} \right) \times 100 \]
\[ \text{Percentage} = 1.6 \times 100 \]
\[ \text{Percentage} = 160\% \]

### Final Answer
Meena's weight is 160% of Tara's weight.

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