P and Q started a business by investing Rs 15000 & Rs (15000 + x) respectively. After four months, Q withdrew 40% of his initial investment. After a year, the total profit was Rs 47000 and the profit share of Q was Rs 22000. Find the value of ‘2x’ .

The correct option is 6000.

Step 1: Understand the Investments over Time

P invested Rs 15000 for the entire year (12 months).

Equivalent investment of P for 1 month =

$15000\×12=180000$

Q initially invested Rs (15000 + x) for 4 months. After 4 months, Q withdrew 40% of his initial investment, leaving 60% of the investment for the remaining 8 months.

Remaining investment of Q =

$60\%\text{of}(15000+x)=0.60\×(15000+x)$

Equivalent investment of Q for 1 month =

$(15000+x)\×4+0.60\×(15000+x)\×8$

$=4(15000+x)+4.8(15000+x)=8.8(15000+x)$

Step 2: Determine Profit Shares

Total Profit = Rs 47000

Profit share of Q = Rs 22000

Profit share of P =

$47000-22000=25000$

Step 3: Equate Ratio of Investments to Ratio of Profits

$\frac{\text{Investment of Q}}{\text{Investment of P}}=\frac{\text{Profit of Q}}{\text{Profit of P}}$

$\frac{8.8(15000+\mathrm{x<mo>)</mo>}}{180000}=\frac{22000}{25000}$

$\frac{8.8(15000+x)}{180000}=\frac{22}{25}$

Solving for (15000 + x):

$8.8(15000+x)=\frac{22\&times;180000}{25}$

$8.8(15000+x)=158400$

$15000+x=\frac{158400}{8.8}$

$15000+\mathrm{x<mo>=</mo><mn>18000</mn>}$

$x=18000-15000=3000$

Step 4: Find the Value of '2x'

$2x=2\&times;3000=6000$

Thus, the value of 2x is 6000.