Some amount of money has to be distributed among A, B and C in the ratio 9:8:6 but by mistake it is distributed in the ratio 1/9 : 1/8 : 1/6 Due to this B losses Rs 1000. Then find the total money which has to be distributed ?

Options

A. 27840
B. 21924
C. 33350
D. 26680

Answer

To solve the problem step by step, we will follow the given information and perform the necessary calculations.

### Step 1: Understand the Ratios
The correct ratio for distributing the money among A, B, and C is given as:
- A : B : C = 9 : 8 : 6

However, the money was mistakenly distributed in the ratio:
- A : B : C = 1/9 : 1/8 : 1/6

### Step 2: Convert the Mistaken Ratio to a Common Form
To compare the two ratios, we need to convert the mistaken ratio into a more manageable form. We will find the least common multiple (LCM) of the denominators (9, 8, and 6).

The LCM of 9, 8, and 6 is 72.

Now we can express the mistaken ratio in terms of this LCM:
- A = (1/9) * 72 = 8
- B = (1/8) * 72 = 9
- C = (1/6) * 72 = 12

So, the mistaken distribution ratio becomes:
- A : B : C = 8 : 9 : 12

### Step 3: Set Up the Total Amount
Let the total amount of money to be distributed be \( X \).

From the correct ratio:
- A's share = \( \frac{9}{23}X \)
- B's share = \( \frac{8}{23}X \)
- C's share = \( \frac{6}{23}X \)

From the mistaken ratio:
- A's share = \( \frac{8}{29}X \)
- B's share = \( \frac{9}{29}X \)
- C's share = \( \frac{12}{29}X \)

### Step 4: Calculate the Loss for B
According to the problem, B loses Rs 1000 due to the incorrect distribution. Therefore, we can set up the equation:

\[ \text{Loss for B} = \text{Correct Share of B} - \text{Mistaken Share of B} \]

Substituting the values we have:

\[ 1000 = \left(\frac{8}{23}X\right) - \left(\frac{9}{29}X\right) \]

### Step 5: Solve the Equation
To solve for \( X \), we first need a common denominator for the fractions. The LCM of 23 and 29 is 667.

Rewriting the equation with a common denominator:

\[ 1000 = \left(\frac{8 \times 29}{667}X\right) - \left(\frac{9 \times 23}{667}X\right) \]

This simplifies to:

\[ 1000 = \frac{232X - 207X}{667} \]

\[ 1000 = \frac{25X}{667} \]

Now, multiplying both sides by 667:

\[ 1000 \times 667 = 25X \]

\[ 667000 = 25X \]

Dividing both sides by 25:

\[ X = \frac{667000}{25} = 26680 \]

### Final Answer
The total amount of money that was supposed to be distributed is **Rs 26680**.

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