A sum of Rs .53 divided among Rohit , Mohit & Shobit in such a way that Rohit gets Rs. 7 more than what Mohit gets and Mohit gets Rs .8 more than what Shobhit gets . The ratio of their shares is :

Options

A. `16:9:18`
B. `25:18:10`
C. `18:25:10`
D. `15:8:30`

Answer

To solve the problem step by step, we will define the shares of Rohit, Mohit, and Shobit in terms of variables and then set up equations based on the information given in the question.

### Step 1: Define the variables
Let:
- Rohit's share = R
- Mohit's share = M
- Shobit's share = S

### Step 2: Set up the total equation
According to the question, the total amount shared among them is Rs. 53. Therefore, we can write:
\[ R + M + S = 53 \]

### Step 3: Set up the relationships based on the information given
1. Rohit gets Rs. 7 more than Mohit:
\[ R = M + 7 \]

2. Mohit gets Rs. 8 more than Shobit:
\[ M = S + 8 \]

### Step 4: Substitute the relationships into the total equation
Now we will substitute the expressions for R and M into the total equation.

From the second equation, we can express M in terms of S:
\[ M = S + 8 \]

Now substitute this into the first equation for R:
\[ R = (S + 8) + 7 = S + 15 \]

Now we can substitute both R and M into the total equation:
\[ (S + 15) + (S + 8) + S = 53 \]

### Step 5: Simplify the equation
Combine like terms:
\[ S + 15 + S + 8 + S = 53 \]
\[ 3S + 23 = 53 \]

### Step 6: Solve for S
Subtract 23 from both sides:
\[ 3S = 53 - 23 \]
\[ 3S = 30 \]

Now divide by 3:
\[ S = 10 \]

### Step 7: Find M and R
Now that we have Shobit's share (S), we can find Mohit's share (M) and Rohit's share (R):
1. Mohit's share:
\[ M = S + 8 = 10 + 8 = 18 \]

2. Rohit's share:
\[ R = M + 7 = 18 + 7 = 25 \]

### Step 8: Write the shares
Now we have:
- Rohit's share (R) = 25
- Mohit's share (M) = 18
- Shobit's share (S) = 10

### Step 9: Find the ratio of their shares
The ratio of their shares R:M:S is:
\[ R:M:S = 25:18:10 \]

### Final Result
Thus, the ratio of their shares is \( 25:18:10 \).

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