R and S started a business by investing Rs 20000 and Rs (20000+y), respectively. After six months, S withdrew 30% of his initial investment. At the end of the year, the total profit was Rs 13200, and the profit share of S was Rs 6800. Find the value of 3y.

The correct answer is 15000.

Let's find the value of $y$ and then calculate $3y$ step-by-step.

Step 1: Understand the investments and their time periods
R's investment is Rs $20000$ for the entire year (12 months).
S's initial investment is Rs $(20000+y)$.
For the first 6 months, S's investment is Rs $(20000+y)$.
After 6 months, S withdraws 30% of his initial investment. Therefore, the remaining investment of S for the next 6 months is:
$70\%\text{of}(20000+y)=0.7(20000+y)$

Step 2: Calculate the ratio of equivalent investments for 1 month
The equivalent investment of R for 1 month is:
$I_R=20000\times 12=240000$
The equivalent investment of S for 1 month is:
$I_S=(20000+y)\times 6+0.7(20000+y)\times 6$
Factoring out $6(20000+y)$:
$I_S=6(20000+y)(1+0.7)=6(20000+y)\left(1.7\right)=10.2(20000+y)$

Step 3: Relate the investment ratio to the profit ratio
The total profit at the end of the year is Rs $13200$.
The profit share of S is Rs $6800$.
Therefore, the profit share of R is:
$13200-6800=6400$
The ratio of profits is equal to the ratio of their equivalent investments:
$\frac{I_S}{I_R}=\frac{\text{Profit of S}}{\text{Profit of R}}$
Substituting the values:
$\frac{10.2(20000+y)}{240000}=\frac{6800}{6400}$

Step 4: Solve for y
Simplify the profit ratio:
$\frac{6800}{6400}=\frac{68}{64}=\frac{17}{16}$
Now set up the equation:
$\frac{10.2(20000+y)}{240000}=\frac{17}{16}$
Multiply both sides by $240000$:
$10.2(20000+y)=\frac{17}{16}\times 240000$
Since $240000/16=15000$:
$10.2(20000+y)=17\times 15000$
$10.2(20000+y)=255000$
Divide by $10.2$:
$20000+y=\frac{255000}{10.2}$
$20000+y=25000$
$y=25000-20000=5000$

Step 5: Find the value of 3y
We need to find the value of $3y$:
$3y=3\times 5000=15000$