By mistake, Instead of dividing Rs 117 among A, B and C in the ratio of `2:3:4`. it was divided in the ratio of `1/2 : 1/3 : 1/4`. Who gains the most and by how much?

Options

A. A)Rs 28
B. B)Rs 3
C. C)Rs 20
D. D)Rs 25

Answer

To solve the problem, we need to compare the amounts received by A, B, and C when the total Rs 117 is divided in two different ratios: the correct ratio of 2:3:4 and the incorrect ratio of 1/2 : 1/3 : 1/4.

### Step 1: Calculate the total parts in the correct ratio (2:3:4)
The correct ratio is 2:3:4.
- Total parts = 2 + 3 + 4 = 9 parts.

### Step 2: Calculate the value of one part in the correct ratio
- Total amount = Rs 117
- Value of one part = Total amount / Total parts = 117 / 9 = Rs 13.

### Step 3: Calculate the amounts received by A, B, and C in the correct ratio
- Amount received by A = 2 parts = 2 × 13 = Rs 26.
- Amount received by B = 3 parts = 3 × 13 = Rs 39.
- Amount received by C = 4 parts = 4 × 13 = Rs 52.

### Step 4: Calculate the total parts in the incorrect ratio (1/2 : 1/3 : 1/4)
To work with the incorrect ratio, we first need to convert it into a common format.
- The denominators are 2, 3, and 4. The LCM of 2, 3, and 4 is 12.
- Convert the ratios:
- 1/2 = 6/12
- 1/3 = 4/12
- 1/4 = 3/12
- So the incorrect ratio becomes 6:4:3.

### Step 5: Calculate the total parts in the incorrect ratio
- Total parts = 6 + 4 + 3 = 13 parts.

### Step 6: Calculate the value of one part in the incorrect ratio
- Value of one part = Total amount / Total parts = 117 / 13 = Rs 9.

### Step 7: Calculate the amounts received by A, B, and C in the incorrect ratio
- Amount received by A = 6 parts = 6 × 9 = Rs 54.
- Amount received by B = 4 parts = 4 × 9 = Rs 36.
- Amount received by C = 3 parts = 3 × 9 = Rs 27.

### Step 8: Determine who gains the most and by how much
Now we compare the amounts received by A, B, and C in both distributions:
- A: Correct = Rs 26, Incorrect = Rs 54 → Gain = 54 - 26 = Rs 28.
- B: Correct = Rs 39, Incorrect = Rs 36 → Loss = 39 - 36 = Rs 3.
- C: Correct = Rs 52, Incorrect = Rs 27 → Loss = 52 - 27 = Rs 25.

### Conclusion
A gains the most with a gain of Rs 28.