P, Q and R invest ₹14000, ₹18000 and ₹24000 respectively to start a business. If the profit at the end of the year is ₹25480, then what is difference between the share of P and Q?

Options

A. ₹2670
B. ₹3480
C. ₹1820
D. ₹2140

Answer

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

### Step 1: Determine the investment amounts
P invests ₹14,000, Q invests ₹18,000, and R invests ₹24,000.

### Step 2: Find the ratio of investments
To find the ratio of their investments, we can express the investments in a simpler form:
- P's investment = 14,000
- Q's investment = 18,000
- R's investment = 24,000

We can divide each amount by 1,000 to simplify:
- P's investment = 14
- Q's investment = 18
- R's investment = 24

Now, we can find the ratio:
- The ratio of P : Q : R = 14 : 18 : 24

Next, we simplify this ratio by dividing each term by 2:
- 14 ÷ 2 = 7
- 18 ÷ 2 = 9
- 24 ÷ 2 = 12

Thus, the simplified ratio of investments is:
- P : Q : R = 7 : 9 : 12

### Step 3: Calculate the total parts in the ratio
Now we add the parts of the ratio together:
- Total parts = 7 + 9 + 12 = 28

### Step 4: Calculate individual shares of profit
The total profit at the end of the year is ₹25,480. Since the profit is distributed in the same ratio as the investments, we can find the share of each person.

- P's share of profit = (P's ratio / Total parts) × Total profit
= (7 / 28) × 25,480
= (1 / 4) × 25,480
= 6,370

- Q's share of profit = (Q's ratio / Total parts) × Total profit
= (9 / 28) × 25,480
= (9 × 25,480) / 28
= 9,810

### Step 5: Calculate the difference between the shares of P and Q
Now, we find the difference between the shares of P and Q:
- Difference = Q's share - P's share
= 9,810 - 6,370
= 3,440

### Conclusion
The difference between the share of P and Q is ₹3,440.

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