Anuj kumar makes 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 and R are respectively:

Answer

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

### Step 1: Calculate the total profit after tax
The total profit made by Anuj Kumar is Rs 9,00,000. Since 20% of this profit is paid as taxes, we first need to calculate the amount paid as taxes.

**Calculation:**
- Tax = 20% of 9,00,000
- Tax = 0.20 × 9,00,000 = 1,80,000

Now, we subtract the tax from the total profit to find the profit after tax.

**Profit after tax:**
- Profit after tax = Total profit - Tax
- Profit after tax = 9,00,000 - 1,80,000 = 7,20,000

### Step 2: Determine the ratio of shares among partners P, Q, and R
The shares of P, Q, and R are given in the ratio of 1 : 1(1/2) : 2. To work with this ratio, we first convert it into a simpler form.

**Conversion of ratio:**
- The ratio can be expressed as 1 : 1.5 : 2.
- To eliminate the decimal, we can multiply each term by 2:
- P = 1 × 2 = 2
- Q = 1.5 × 2 = 3
- R = 2 × 2 = 4

Thus, the ratio becomes 2 : 3 : 4.

### Step 3: Calculate the total parts in the ratio
Now, we need to find the total number of parts in the ratio.

**Total parts:**
- Total parts = 2 + 3 + 4 = 9

### Step 4: Calculate the share of each partner
Now we can calculate the share of each partner by dividing the profit after tax according to the ratio.

**Calculation of shares:**
- Share of P = (2/9) × 7,20,000
- Share of Q = (3/9) × 7,20,000
- Share of R = (4/9) × 7,20,000

**Calculating each share:**
1. Share of P:
- Share of P = (2/9) × 7,20,000 = 1,60,000
2. Share of Q:
- Share of Q = (3/9) × 7,20,000 = 2,40,000
3. Share of R:
- Share of R = (4/9) × 7,20,000 = 3,20,000

### Final Shares:
- Share of P = Rs 1,60,000
- Share of Q = Rs 2,40,000
- Share of R = Rs 3,20,000

### Summary:
The shares of P, Q, and R are respectively Rs 1,60,000, Rs 2,40,000, and Rs 3,20,000.

---