Q.P and Q invest $25000$ rupees and $35000$ rupees respectively for one year. If the profit for the year is $18000$ rupees, find the share of each.

Equal times mean the profit is shared simply in the ratio of the two capitals.

One part is worth $18000/12 = 1500$ rupees, and P takes $5$ parts while Q takes $7$.

Both capitals are invested for the same year, so this is a simple partnership and profit is shared in the ratio of the capitals.

Step 1 — capital ratio. $25000 : 35000 = 5 : 7 \quad (\text{dividing both by } 5000).$

Step 2 — value of one part. Total parts $= 5 + 7 = 12$, so $\text{one part} = \frac{18000}{12} = 1500 \text{ rupees}.$

Step 3 — each share. $P = 5 \times 1500 = 7500, \qquad Q = 7 \times 1500 = 10500 \text{ rupees}.$

Verification. $7500 + 10500 = 18000$ rupees (the full profit), and $7500 : 10500 = 5 : 7$ matches the capital ratio — both confirm the answer.

As fractions: $P = \frac{5}{12}\times 18000 = 7500$ and $Q = \frac{7}{12}\times 18000 = 10500$ rupees.

Reducing $25000:35000$ carelessly to $5:6$ or leaving it unreduced are the usual slips — divide both terms by their highest common factor ($5000$) to get the correct $5:7$.