Question

Two persons P and Q enter into partnership with capitals of ₹60000 and ₹45000 respectively. After three months P withdrew ₹20000 while Q invested another ₹15000. After another five months R joins the business with a capital of ₹90000. At the end of the year the difference between the profits received by P and R in a total profit of ₹32200 in rupees is

• A. 4590
• B. 4250
• C. 3680
• D. 3340

Hint:

In partnership questions involving changes in investment, split the year into intervals and calculate Capital × Time separately for each interval before forming the final ratio.

Answer 1

The Correct Option is C

Concept: Profit in a partnership is divided in the ratio of capital invested multiplied by the duration for which that capital remained invested.

Step 1: Calculate P's capital-months.
For first 3 months, \[ 60000\times3=180000 \] After withdrawing ₹20000, capital becomes ₹40000 for remaining 9 months. \[ 40000\times9=360000 \] Therefore, \[ P=180000+360000 \] \[ =540000 \]

Step 2: Calculate Q's capital-months.
For first 3 months, \[ 45000\times3=135000 \] After adding ₹15000, capital becomes ₹60000 for remaining 9 months. \[ 60000\times9=540000 \] Thus, \[ Q=135000+540000 \] \[ =675000 \]

Step 3: Calculate R's capital-months.
R joins after \(3+5=8\) months. Therefore R remains for \[ 12-8=4 \text{ months} \] Hence, \[ R=90000\times4 \] \[ =360000 \]

Step 4: Find the profit sharing ratio.
\[ P:Q:R = 540000:675000:360000 \] Dividing by 45000, \[ 12:15:8 \] Total ratio units \[ =12+15+8 \] \[ =35 \]

Step 5: Calculate the difference between P's and R's profits.
Difference in ratio units \[ =12-8=4 \] Therefore difference in profit \[ =\frac{4}{35}\times32200 \] \[ =4\times920 \] \[ =3680 \] Hence the required difference is \[ \boxed{₹3680} \]