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 both the years are same for T and S, then find the return from T & S when calulated after 1 year.

The correct answer is Rs. 24,300.

Step 1: Extract the stock values for S and T from the bar graph.
From the given bar graph, the percentage distribution of stocks sold to each person is:
S = 25%
T = 5%
The total stock value of Ram is Rs. 3,60,000.
We calculate the individual stock values for S and T:
$\text{Stock Value of S}=\; 25\%\; \backslash text\{\; of\; \}\; 3,60,000\; =\; \backslash frac\{25\}\{100\}\; \backslash times\; 3,60,000\; =\; \backslash text\{Rs.\; \}\; 90,000$
$\text{Stock Value of T}=\; 5\%\; \backslash text\{\; of\; \}\; 3,60,000\; =\; \backslash frac\{5\}\{100\}\; \backslash times\; 3,60,000\; =\; \backslash text\{Rs.\; \}\; 18,000$

Step 2: Find the percentage increment after 1 year for T and S.
Let the percentage increment for both years be equal. If the annual increment rate is r%, the overall increment over two successive years is given by the formula:
$\text{Overall Increment \%}=\; r\; +\; r\; +\; \backslash frac\{r^2\}\{100\}\; =\; 2r\; +\; \backslash frac\{r^2\}\{100\}$

For S:
The table shows that the overall increment percentage for S is 44%. Let the annual increment for S be $r_S$:
$2r\_S\; +\; \backslash frac\{r\_S^2\}\{100\}\; =\; 44$
$r\_S^2\; +\; 200r\_S\; -\; 4400\; =\; 0$
$(r\_S\; +\; 220)(r\_S\; -\; 20)\; =\; 0$
Taking the positive root, we get:
$r\_S\; =\; 20\%$ (which matches the 20% for the 1st year listed in the table).

For T:
The table shows that the overall increment percentage for T is 82.25%. Let the annual increment for T be $r_T$:
$2r\_T\; +\; \backslash frac\{r\_T^2\}\{100\}\; =\; 82.25$
$r\_T^2\; +\; 200r\_T\; -\; 8225\; =\; 0$
Using the quadratic formula to solve for $r_T$:
$r\_T\; =\; \backslash frac\{-200\; \backslash pm\; \backslash sqrt\{200^2\; -\; 4\; \backslash times\; 1\; \backslash times\; (-8225)\}\}\{2\}$
$r\_T\; =\; \backslash frac\{-200\; \backslash pm\; \backslash sqrt\{40000\; +\; 32900)\}\}\{2\}$
$r\_T\; =\; \backslash frac\{-200\; \backslash pm\; \backslash sqrt\{72900\}\}\{2\}$
Since
$r\_T\; =\; \backslash frac\{-200\; +\; 270\}\{2\}\; =\; \backslash frac\{70\}\{2\}\; =\; 35\%$

Step 3: Calculate the return from T and S after 1 year.
The return after 1 year is calculated using the first-year percentage increment on the initial stock value:
$\text{Return from S}=\; 20\%\; \backslash text\{\; of\; \}\; 90,000\; =\; \backslash frac\{20\}\{100\}\; \backslash times\; 90,000\; =\; \backslash text\{Rs.\; \}\; 18,000$
$\text{Return from T}=\; 35\%\; \backslash text\{\; of\; \}\; 18,000\; =\; \backslash frac\{35\}\{100\}\; \backslash times\; 18,000\; =\; \backslash text\{Rs.\; \}\; 6,300$
$\text{Total Return}=\; \backslash text\{Return\; from\; S\}\; +\; \backslash text\{Return\; from\; T\}\; =\; 18,000\; +\; 6,300\; =\; \backslash text\{Rs.\; \}\; 24,300$