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P, Q, and R enter into a partnership. P contributes one-fifth of the whole capital while Q contributes twice as much as P and R together contribute. If the profit at the end of the year is ₹555540, what is the difference (in ₹) of Q's share and the combined share of P and R in the profit?

Solution

✅ Correct Option: 1

Total Profit: ₹ 5,55,540

Q contributes twice as much as P and R together.

P contributes 15\frac{1}{5} of the capital (Note: This information is extra and not required to find the specific difference requested).


Since profit is distributed based on capital contribution, we look at the relationship between Q and the combined capital of P and R.

Q=2×(P+R)Q = 2 \times (P + R)

This can be written as a ratio:

EntityShare RatioFraction of Total
Q2223\frac{2}{3}
P + R1113\frac{1}{3}
Total31

The difference between Q's share and the combined share of (P + R):

Difference=Share of Q−Share of (P + R)\text{Difference} = \text{Share of Q} - \text{Share of (P + R)}

Difference=23(Total Profit)−13(Total Profit)\text{Difference} = \frac{2}{3}(\text{Total Profit}) - \frac{1}{3}(\text{Total Profit})

Difference=13×Total Profit\text{Difference} = \frac{1}{3} \times \text{Total Profit}

Difference=13×5,55,540\text{Difference} = \frac{1}{3} \times 5,55,540

Difference=1,85,180\text{Difference} = 1,85,180

Therefore, the difference between Q's share and the combined share of P and R is ₹ 1,85,180.

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