A sum of Rs 4,360 was to be divided among A, B, C and D in the ratio of 3 : 4 : 5 : 8, but it was divided in the ratio `(1)/(3) : (1)/(4) : (1)/(5) : (1)/(8)` by mistake.
Which of the following statements will hold true as a result?
(a)C received Rs 130 less
(b)D received Rs 1,144 more
(c)A received Rs 956 more
(d)B received Rs 318 less

Options

A. B received Rs 318 less
B. D received Rs 1,144 more
C. A received Rs 956
D. C received Rs 130 less

Answer

To solve the problem, we will follow these steps:

### Step 1: Determine the total ratio for the intended distribution
The intended ratio for A, B, C, and D is given as 3:4:5:8.

### Step 2: Calculate the total parts in the intended ratio
Total parts = 3 + 4 + 5 + 8 = 20 parts.

### Step 3: Calculate the value of one part
Total amount = Rs 4,360.
Value of one part = Total amount / Total parts = 4360 / 20 = Rs 218.

### Step 4: Calculate the amount each person should receive based on the intended ratio
- A's share = 3 parts = 3 * 218 = Rs 654.
- B's share = 4 parts = 4 * 218 = Rs 872.
- C's share = 5 parts = 5 * 218 = Rs 1090.
- D's share = 8 parts = 8 * 218 = Rs 1744.

### Step 5: Determine the mistaken ratio
The mistaken ratio is given as (1/3):(1/4):(1/5):(1/8).

### Step 6: Convert the mistaken ratio to a common format
To convert these fractions to a common ratio, we find the LCM of the denominators (3, 4, 5, 8), which is 120.

- A's mistaken share = 120 / 3 = 40.
- B's mistaken share = 120 / 4 = 30.
- C's mistaken share = 120 / 5 = 24.
- D's mistaken share = 120 / 8 = 15.

### Step 7: Calculate the total parts in the mistaken distribution
Total parts = 40 + 30 + 24 + 15 = 109 parts.

### Step 8: Calculate the value of one part in the mistaken distribution
Value of one part = Total amount / Total parts = 4360 / 109 = Rs 40.

### Step 9: Calculate the amount each person received based on the mistaken ratio
- A's mistaken share = 40 parts = 40 * 40 = Rs 1600.
- B's mistaken share = 30 parts = 30 * 40 = Rs 1200.
- C's mistaken share = 24 parts = 24 * 40 = Rs 960.
- D's mistaken share = 15 parts = 15 * 40 = Rs 600.

### Step 10: Compare the amounts received by each person
- C's intended share = Rs 1090, but received = Rs 960.
- Difference for C = 1090 - 960 = Rs 130 less.

### Conclusion
The correct statement is (a) C received Rs 130 less.