A company make a profit of ₹ 9,00,000, `20 %` of which is 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 & R :-

Options

A. 240000, 320000, 160000
B. 320000, 240000, 160000
C. 160000, 320000, 240000
D. 160000, 240000, 320000

Answer

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

### Step 1: Calculate the amount paid as tax
The company makes a profit of ₹9,00,000, and 20% of this profit is paid as tax.

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

### Step 2: Calculate the remaining profit after tax
Now, we need to find out how much profit remains after paying the tax.

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

### Step 3: Understand the ratio in which the remaining profit is divided
The remaining profit of ₹7,20,000 is to be divided among partners P, Q, and R in the ratio of \(1 : 1 : \frac{1}{2} : 2\). First, we need to convert this ratio into a simpler form.

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

To simplify, we can multiply each part by 2 to eliminate the fraction:
- P = 2 parts
- Q = 2 parts
- R = 1 part
- R = 4 parts

Thus, the simplified ratio becomes:
\[ P : Q : R = 2 : 2 : 4 \]

### Step 4: Calculate the total parts in the ratio
Now, we add up the parts in the ratio:
\[ \text{Total Parts} = 2 + 2 + 4 = 8 \]

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

\[ \text{Value of each part} = \frac{\text{Remaining Profit}}{\text{Total Parts}} = \frac{7,20,000}{8} = 90,000 \]

### Step 6: Calculate the shares of P, Q, and R
Now we can find the shares of P, Q, and R by multiplying the value of each part by the number of parts each partner has.

- Share of P:
\[ \text{Share of P} = 2 \times 90,000 = 1,80,000 \]

- Share of Q:
\[ \text{Share of Q} = 2 \times 90,000 = 1,80,000 \]

- Share of R:
\[ \text{Share of R} = 4 \times 90,000 = 3,60,000 \]

### Final Shares
- Share of P = ₹1,80,000
- Share of Q = ₹1,80,000
- Share of R = ₹3,60,000

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