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 (Option 3).

Step-by-step Explanation:

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

$\text{Stock value of Q}=\frac{20}{100}\times \mathrm{3,60,000}=\text{Rs. 72,000}$

2. Find the annual percentage increment for Q:
From the table, the overall percentage increment in the price of stocks for Q over two years is 69%.
We are given that the percentage increment for Q is the same for both years. Let this percentage increment be $x\%$.
Using the successive percentage change formula, the overall percentage increment is given by:

$x+x+\frac{x\times x}{100}=69$

$2x+\frac{x^2}{100}=69$

$x^2+200x-6900=0$

$(x+230)(x-30)=0$

Since the percentage increment must be positive, we get:
$x=30$

Thus, the percentage increment for Q is 30% in both the first and second years.

3. Calculate the returns after the 1st and 2nd years:
The return is equal to the price increment.
Return from Q after 1st year (based on the 1st year's increment of 30%):

$\text{Return after 1st year}=30\%\text{of Rs. 72,000}=\frac{30}{100}\times \mathrm{72,000}=\text{Rs. 21,600}$

Return from Q after 2nd year (based on the overall 2-year increment of 69%):

$\text{Return after 2nd year}=69\%\text{of Rs. 72,000}=\frac{69}{100}\times \mathrm{72,000}=\text{Rs. 49,680}$

4. Calculate the difference:
Difference between the return after the 2nd year and the return after the 1st year:

$\text{Difference}=\text{Rs. 49,680}-\text{Rs. 21,600}=\text{Rs. 28,080}$