Directions (64-66): Read the following bar graph and the table carefully and answer the given question:

The bar graph shows the percentage distribution of the stocks sold by Ram to six different people(P , Q, R, S, T and U). Total stock value of Ram is Rs. 3,60,000. Table shows the percentage increment in the price of stocks in two years and the overall percentage increment in the price of stocks. Ram earned some return amount from the each person on the increased price.

Note: % increase in Price = % of the return

If the percentage increment for Q is same for both the years, then find the difference between the return from Q after 1st year and return from after 2nd year.

The correct answer is Rs. 28,080.

Let us break down the solution step-by-step:

Step 1: Calculate the value of stocks sold to Q
From the given bar graph, the percentage distribution of stocks sold to Q is 20%.
The total stock value of Ram is Rs. 3,60,000.
Therefore, the initial stock value of Q is:
Stock value of Q = 20% of 3,60,000

$\text{Stock value of Q}=\frac{20}{100}\times 360000=\text{Rs.}72000$

Step 2: Find the yearly percentage increment for Q
From the table, the overall percentage increment in the price of stocks for Q over two years is 69%.
Let the percentage increment for Q be x% for both years. Using the formula for successive percentage increases:

$x+x+\frac{x\times x}{100}=69$
Multiplying the entire equation by 100 to clear the fraction:

$200x+x^2=6900$
Rearranging it into a quadratic equation:

$x^2+200x-6900=0$
Factoring the quadratic equation:

$x^2-30x+230x-6900=0$
$x(x-30)+230(x-30)=0$
$(x-30)(x+230)=0$
This gives:

$x=30\text{ or }x=-230$
Since the percentage increment must be positive, we reject the negative value. Thus, the percentage increment for Q is 30% per year.

Step 3: Calculate the return from Q after the 1st year
The return percentage after the 1st year is equal to the 1st year's price increment (30%).
Return from Q after 1st year = 30% of Rs. 72,000

$\text{Return after 1st year}=\frac{30}{100}\times 72000=\text{Rs.}21600$

Step 4: Calculate the return from Q after the 2nd year
The overall return percentage after the 2nd year is equal to the overall percentage increment in the price of stocks (69%).
Return from Q after 2nd year = 69% of Rs. 72,000

$\text{Return after 2nd year}=\frac{69}{100}\times 72000=\text{Rs.}49680$

Step 5: Find the difference between the returns
Difference = (Return after 2nd year) - (Return after 1st year)

$\text{Difference}=49680-21600=\text{Rs.}28080$