Mukesh has twice as much moncy as Soham. Soham has 50% more money than Pankaj. If the average money with them is Rs.110, then Mukesh has

Options

A. A) Rs.155
B. B) Rs.160
C. C) Rs.180
D. D) Rs.175

Answer

To solve the problem step by step, we will break down the information given and use it to find out how much money Mukesh has.

### Step 1: Define the variables
Let:
- Pankaj's money = \( P \)
- Soham's money = \( S \)
- Mukesh's money = \( M \)

From the problem, we know:
1. Mukesh has twice as much money as Soham:
\[ M = 2S \]
2. Soham has 50% more money than Pankaj:
\[ S = P + 0.5P = 1.5P \]

### Step 2: Express all amounts in terms of Pankaj's money
From the second equation, we can express Soham's money in terms of Pankaj's money:
\[ S = 1.5P \]
Now substituting \( S \) in the equation for Mukesh:
\[ M = 2S = 2(1.5P) = 3P \]

### Step 3: Calculate the total money
Now we have all the amounts expressed in terms of \( P \):
- Pankaj's money = \( P \)
- Soham's money = \( 1.5P \)
- Mukesh's money = \( 3P \)

The total money with Mukesh, Soham, and Pankaj is:
\[ \text{Total} = M + S + P = 3P + 1.5P + P = 5.5P \]

### Step 4: Find the average money
The average money with them is given as Rs. 110. Since there are 3 people, we can set up the equation:
\[ \frac{5.5P}{3} = 110 \]

### Step 5: Solve for P
To find \( P \), we multiply both sides by 3:
\[ 5.5P = 330 \]
Now, divide by 5.5:
\[ P = \frac{330}{5.5} = 60 \]

### Step 6: Calculate Mukesh's money
Now that we have \( P \), we can find Mukesh's money:
\[ M = 3P = 3 \times 60 = 180 \]

### Final Answer
Mukesh has Rs. 180.

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