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.

Let us solve the problem step-by-step.
Let the investment of P be $I_P=15000$ Rs.
Let the initial investment of Q be $I_Q=15000+x$ Rs.

P invested Rs 15000 for the entire year (12 months).
Therefore, the equivalent investment of P for 1 month is:
$E_P=15000\times 12=180000$

Q invested Rs $(15000+x)$ for the first 4 months.
After 4 months, Q withdrew 40% of his initial investment, which means Q kept $100\%-40\%=60\%$ of his initial investment for the remaining 8 months of the year.
The remaining investment of Q is:
$0.60\times (15000+x)=9000+0.6x$

Therefore, the equivalent investment of Q for 1 month is:
$E_Q=(15000+x)\times 4+(9000+0.6x)\times 8$
$E_Q=60000+4x+72000+4.8x$
$E_Q=132000+8.8x$

The total profit after a year is Rs 47000.
The profit share of Q is Rs 22000.
Therefore, the profit share of P is:
$\text{Profit of P}=47000-22000=25000$ Rs.

Since the profit sharing ratio is equal to the ratio of their equivalent investments:
$\frac{E_P}{E_Q}=\frac{\text{Profit of P}}{\text{Profit of Q}}$
$\frac{180000}{132000+8.8x}=\frac{25000}{22000}$

Simplifying the profit ratio:
$\frac{25000}{22000}=\frac{25}{22}$

Now, equate the two ratios:
$\frac{180000}{132000+8.8x}=\frac{25}{22}$
Cross-multiplying:
$25\times (132000+8.8x)=22\times 180000$
$3300000+220x=3960000$
$220x=3960000-3300000$
$220x=660000$
$x=\frac{660000}{220}$
$x=3000$

We need to find the value of '2x':
$2x=2\times 3000=6000$