Two persons P and Q enter into a business. P puts ₹14,000 more than Q, but P has invested for 8 months and Q has invested for 10 months. If P’s share…

Correct Option

Let P's capital be P and Q's capital be Q.

Based on the problem statement:

• P's capital is ₹14,000 more than Q's: P = Q + 14000, or Q = P – 14000.
• P invested for 8 months.
• Q invested for 10 months.
• Total profit = ₹2,000.
• P's share of profit (S_P) is ₹400 more than Q's share (S_Q).

First, determine the individual profit shares:

• The sum of profit shares is the total profit: S_P + S_Q = 2000.
• Given S_P = S_Q + 400.
• Substituting S_P into the sum equation: (S_Q + 400) + S_Q = 2000.
• This simplifies to 2S_Q = 1600, so S_Q = ₹800.
• Consequently, S_P = 800 + 400 = ₹1200.

The profit sharing ratio is directly proportional to the product of capital and time invested:

$\frac{\text{P's Capital} \times \text{P's Time}}{\text{Q's Capital} \times \text{Q's Time}} = \frac{\text{P's Profit Share}}{\text{Q's Profit Share}}$Q’s Capital×Q’s TimeP’s Capital×P’s Time​=Q’s Profit ShareP’s Profit Share​

Substitute the known values:

$\frac{P \times 8}{(P - 14000) \times 10} = \frac{1200}{800}$(P−14000)×10P×8​=8001200​

Simplify the profit ratio $\frac{1200}{800} = \frac{3}{2}$8001200​=23​:

$\frac{8P}{10(P - 14000)} = \frac{3}{2}$10(P−14000)8P​=23​

Cross-multiply to solve for P:

$\Rightarrow$⇒ $2 \times 8P = 3 \times 10(P - 14000)$2×8P=3×10(P−14000)

$\Rightarrow$⇒ $16P = 30(P - 14000)$16P=30(P−14000)

$\Rightarrow$⇒ $16P = 30P - 420000$16P=30P−420000

$\Rightarrow$⇒ $420000 = 30P - 16P$420000=30P−16P

$\Rightarrow$⇒ $420000 = 14P$420000=14P

$\Rightarrow$⇒ $P = \frac{420000}{14}$P=14420000​

$\Rightarrow$⇒ P = 30000

Therefore, the capital contributed by P is ₹30,000.

Incorrect Options

Options 2 (₹26,000), 3 (₹24,000), and 4 (₹20,000) are incorrect. These values for P's capital do not satisfy the conditions derived from the investment terms and the specified profit distribution between P and Q.