A sum of Rs 2720 has to be divided among Jati Nitin and Sumit such that Jatin gets `2/3` of what Nitin gets and Nitin gets `1/4` of what Sumit gets. Find the share of Jatin.

Options

A. Rs 1960
B. Rs 320
C. Rs 640
D. Rs 1260

Answer

To solve the problem of dividing Rs 2720 among Jatin, Nitin, and Sumit, we will follow these steps:

### Step 1: Define Variables
Let the amount that Sumit gets be denoted as \( X \).

### Step 2: Express Nitin's Share
According to the problem, Nitin gets \( \frac{1}{4} \) of what Sumit gets. Therefore, Nitin's share can be expressed as:
\[ \text{Nitin's share} = \frac{1}{4} X \]

### Step 3: Express Jatin's Share
It is also given that Jatin gets \( \frac{2}{3} \) of what Nitin gets. Thus, Jatin's share can be expressed as:
\[ \text{Jatin's share} = \frac{2}{3} \left(\frac{1}{4} X\right) = \frac{2X}{12} = \frac{X}{6} \]

### Step 4: Set Up the Equation
The total amount distributed among Jatin, Nitin, and Sumit is Rs 2720. Therefore, we can set up the equation:
\[ X + \frac{1}{4}X + \frac{X}{6} = 2720 \]

### Step 5: Find a Common Denominator
To solve the equation, we need a common denominator for the fractions. The least common multiple (LCM) of 1, 4, and 6 is 12. We can rewrite the equation as:
\[ \frac{12X}{12} + \frac{3X}{12} + \frac{2X}{12} = 2720 \]

### Step 6: Combine the Terms
Now, combine the terms on the left side:
\[ \frac{12X + 3X + 2X}{12} = 2720 \]
\[ \frac{17X}{12} = 2720 \]

### Step 7: Solve for X
To isolate \( X \), multiply both sides by 12:
\[ 17X = 2720 \times 12 \]
\[ 17X = 32640 \]
Now, divide both sides by 17:
\[ X = \frac{32640}{17} = 1920 \]

### Step 8: Calculate Jatin's Share
Now that we have \( X \), we can find Jatin's share:
\[ \text{Jatin's share} = \frac{X}{6} = \frac{1920}{6} = 320 \]

### Final Answer
Thus, Jatin's share is Rs 320.

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