A company make of profit of Rs. 9,00,000 , 20% of which a paid as taxes. If the rest is divided among the partners P,Q and R in the ratio of `1:1 1/2 :2`, then the shares of P,Q and R are respectively

Options

A. 2,40,000,3,20,000,1,60,000
B. 3,20,000,2,40,000,1,60,000
C. 1,60,000,3,20,000,2,40,000
D. 1,60,000,2,40,000,3,20,000

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the amount paid as taxes.
The company made a profit of Rs. 9,00,000 and pays 20% of this amount as taxes.

\[ \text{Tax amount} = 20\% \text{ of } 9,00,000 = \frac{20}{100} \times 9,00,000 = 1,80,000 \]

### Step 2: Calculate the remaining profit after taxes.
Now, we subtract the tax amount from the total profit to find the remaining profit.

\[ \text{Remaining profit} = \text{Total profit} - \text{Tax amount} = 9,00,000 - 1,80,000 = 7,20,000 \]

### Step 3: Determine the ratio in which the remaining profit is divided.
The remaining profit of Rs. 7,20,000 is divided among partners P, Q, and R in the ratio of \(1 : \frac{3}{2} : 2\). To make calculations easier, we convert the ratio into whole numbers.

The ratio can be expressed as:
- P = 1
- Q = \( \frac{3}{2} \) = 1.5
- R = 2

To eliminate the fraction, we can multiply the entire ratio by 2:
- P = \(1 \times 2 = 2\)
- Q = \(1.5 \times 2 = 3\)
- R = \(2 \times 2 = 4\)

Thus, the new ratio is \(2 : 3 : 4\).

### Step 4: Calculate the total parts in the ratio.
Now, we add the parts of the ratio together.

\[ \text{Total parts} = 2 + 3 + 4 = 9 \]

### Step 5: Calculate the value of each part.
Now, we can find the value of each part by dividing the remaining profit by the total number of parts.

\[ \text{Value of each part} = \frac{\text{Remaining profit}}{\text{Total parts}} = \frac{7,20,000}{9} = 80,000 \]

### Step 6: Calculate the shares of P, Q, and R.
Now we can calculate the individual shares of P, Q, and R by multiplying the value of each part by their respective parts.

- Share of P:
\[ \text{Share of P} = 2 \times 80,000 = 1,60,000 \]

- Share of Q:
\[ \text{Share of Q} = 3 \times 80,000 = 2,40,000 \]

- Share of R:
\[ \text{Share of R} = 4 \times 80,000 = 3,20,000 \]

### Final Result
Thus, the shares of P, Q, and R are:
- P = Rs. 1,60,000
- Q = Rs. 2,40,000
- R = Rs. 3,20,000