P, Q and R have a certain amount of money with themselves. Q has `50%` more than what P has and R has `1/3` of what Q has. If P, Q and R together have ₹240 then how much money does P alone have?( in ₹)

Options

A. 75
B. 60
C. 120
D. 80

Answer

To solve the problem step by step, we will define the amounts of money that P, Q, and R have in terms of P.

### Step 1: Define the amount P has
Let the amount of money that P has be denoted as \( P \).

### Step 2: Express the amount Q has in terms of P
According to the problem, Q has 50% more than what P has. Therefore, we can express Q's amount as:
\[ Q = P + 0.5P = \frac{3P}{2} \]

### Step 3: Express the amount R has in terms of Q
The problem states that R has \( \frac{1}{3} \) of what Q has. Thus, we can express R's amount as:
\[ R = \frac{1}{3}Q = \frac{1}{3} \times \frac{3P}{2} = \frac{P}{2} \]

### Step 4: Set up the equation for the total amount
Now, we know that P, Q, and R together have ₹240. Therefore, we can write the equation:
\[ P + Q + R = 240 \]
Substituting the expressions for Q and R in terms of P, we get:
\[ P + \frac{3P}{2} + \frac{P}{2} = 240 \]

### Step 5: Combine the terms
To combine the terms, we can convert all terms to have a common denominator:
\[ P = \frac{2P}{2}, \quad Q = \frac{3P}{2}, \quad R = \frac{P}{2} \]
So the equation becomes:
\[ \frac{2P}{2} + \frac{3P}{2} + \frac{P}{2} = 240 \]
Combining these gives:
\[ \frac{2P + 3P + P}{2} = 240 \]
\[ \frac{6P}{2} = 240 \]

### Step 6: Simplify the equation
Now, simplifying the left side:
\[ 3P = 240 \]

### Step 7: Solve for P
To find the value of P, divide both sides by 3:
\[ P = \frac{240}{3} = 80 \]

### Conclusion
Thus, the amount of money that P has is ₹80.