`1/4`th of Nikhil’s money is equal to `1/6`th of Yogesh’s money. If both together have `Rs. 600` , the difference between their amounts is -

Options

A. Rs. 50
B. Rs. 120
C. Rs. 240
D. Rs. 360

Answer

To solve the problem, we need to follow these steps:

### Step 1: Set up the equations based on the problem statement.
Let Nikhil's money be \( X \) and Yogesh's money be \( Y \). According to the problem, we have:
\[ \frac{1}{4}X = \frac{1}{6}Y \]
Also, we know that together they have Rs. 600:
\[ X + Y = 600 \]

### Step 2: Express \( Y \) in terms of \( X \).
From the second equation, we can express \( Y \) as:
\[ Y = 600 - X \]

### Step 3: Substitute \( Y \) in the first equation.
Now, substitute \( Y \) in the first equation:
\[ \frac{1}{4}X = \frac{1}{6}(600 - X) \]

### Step 4: Cross-multiply to eliminate the fractions.
Cross-multiplying gives us:
\[ 6 \cdot \frac{1}{4}X = 1 \cdot (600 - X) \]
This simplifies to:
\[ \frac{6}{4}X = 600 - X \]
or
\[ \frac{3}{2}X = 600 - X \]

### Step 5: Rearrange the equation.
To eliminate the fraction, multiply the entire equation by 2:
\[ 3X = 1200 - 2X \]

### Step 6: Combine like terms.
Now, add \( 2X \) to both sides:
\[ 3X + 2X = 1200 \]
This simplifies to:
\[ 5X = 1200 \]

### Step 7: Solve for \( X \).
Now, divide both sides by 5:
\[ X = \frac{1200}{5} = 240 \]

### Step 8: Find \( Y \).
Now that we have \( X \), we can find \( Y \):
\[ Y = 600 - X = 600 - 240 = 360 \]

### Step 9: Calculate the difference between their amounts.
The difference between their amounts is:
\[ Y - X = 360 - 240 = 120 \]

### Final Answer:
The difference between Nikhil's and Yogesh's amounts is Rs. 120.

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