A sum of Rs 53 is divided amongst A, B and C in such a way that A gets Rs 7 more than B gets and B gets Rs 8 more than C gets, the ratio of their shares is

Options

A. `6:7:8`
B. `25:18:10`
C. `12:14:9`
D. None of these

Answer

To solve the problem step by step, we will define the amounts received by A, B, and C based on the information given.

### Step 1: Define the variables
Let:
- C = amount received by C
- B = amount received by B
- A = amount received by A

### Step 2: Establish relationships based on the problem
From the problem:
- A gets Rs 7 more than B:
\( A = B + 7 \)
- B gets Rs 8 more than C:
\( B = C + 8 \)

### Step 3: Substitute B in terms of C into the equation for A
Substituting the expression for B into the equation for A gives:
\( A = (C + 8) + 7 \)
Thus,
\( A = C + 15 \)

### Step 4: Write the total amount equation
According to the problem, the total amount shared by A, B, and C is Rs 53:
\( A + B + C = 53 \)

### Step 5: Substitute A and B in terms of C into the total amount equation
Now substituting the expressions for A and B into the total amount equation:
\( (C + 15) + (C + 8) + C = 53 \)

### Step 6: Simplify the equation
Combine like terms:
\( 3C + 23 = 53 \)

### Step 7: Solve for C
Subtract 23 from both sides:
\( 3C = 30 \)
Now divide by 3:
\( C = 10 \)

### Step 8: Find the amounts for B and A
Now that we have C, we can find B and A:
- For B:
\( B = C + 8 = 10 + 8 = 18 \)
- For A:
\( A = B + 7 = 18 + 7 = 25 \)

### Step 9: Write the amounts received by A, B, and C
Now we have:
- A = 25
- B = 18
- C = 10

### Step 10: Find the ratio of their shares
The ratio of A, B, and C is:
\( A : B : C = 25 : 18 : 10 \)

### Final Answer
The ratio of their shares is \( 25 : 18 : 10 \).

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