Read the paragraph carefully and answer the following questions.
Two general stores P & Q sells five items i.e. A, B, C, D & E. Total number of items sold by these two stores is 8400 and ratio between total items sold by store P to store Q is 3:4. Total item A sold by store P is `16(2)/(3)%` more than total item D sold by that store, while total item C sold by store P is 160 less than total item D sold by store P. Total item B sold by store P is `77(7)/(9)%` more than total item D sold by store P and total number of item E sold by store P is 1080 less than that of item B sold by store P. Total item D & item B sold by store Q is 240 and 12.5 % more than same items sold by store P respectively. Respective ratio of total item A, C & E sold by store Q is 26:23: 11.
Total item E sold by store Q is what percent more than that of total number of same item sold by store P?

Options

A. `75%`
B. `115%`
C. `125%`
D. `120%`

Answer

To solve the problem step by step, we will break down the information provided and calculate the required values systematically.

### Step 1: Determine the total items sold by each store
The total items sold by stores P and Q is 8400, and the ratio of items sold by P to Q is 3:4.

Let the total items sold by store P be \(3x\) and by store Q be \(4x\).
Thus, we have:
\[ 3x + 4x = 8400 \]
\[ 7x = 8400 \]
\[ x = \frac{8400}{7} = 1200 \]

Now, we can find the total items sold by each store:
- Total items sold by store P:
\[ 3x = 3 \times 1200 = 3600 \]
- Total items sold by store Q:
\[ 4x = 4 \times 1200 = 4800 \]

### Step 2: Define variables for items sold at store P
Let:
- Total items D sold by store P = \(D\)
- Total items A sold by store P = \(A\)
- Total items C sold by store P = \(C\)
- Total items B sold by store P = \(B\)
- Total items E sold by store P = \(E\)

From the problem:
1. \(A\) is \(16 \frac{2}{3}\% = \frac{50}{3}\%\) more than \(D\):
\[ A = D + \frac{50}{3} \cdot D = \frac{350}{3}D \]

2. \(C\) is 160 less than \(D\):
\[ C = D - 160 \]

3. \(B\) is \(77 \frac{7}{9}\% = \frac{700}{9}\%\) more than \(D\):
\[ B = D + \frac{700}{9} \cdot D = \frac{1600}{9}D \]

4. \(E\) is 1080 less than \(B\):
\[ E = B - 1080 = \frac{1600}{9}D - 1080 \]

### Step 3: Set up the equation for total items sold by store P
Now, we can write the equation for the total items sold by store P:
\[ A + B + C + D + E = 3600 \]
Substituting the expressions we derived:
\[ \frac{350}{3}D + \frac{1600}{9}D + (D - 160) + D + \left(\frac{1600}{9}D - 1080\right) = 3600 \]

### Step 4: Simplify and solve for \(D\)
Combine all the terms:
\[ \left(\frac{350}{3} + \frac{1600}{9} + 1 + 1 + \frac{1600}{9} - 160 - 1080\right)D = 3600 \]
To simplify, convert all fractions to a common denominator (which is 9):
\[ \frac{1050}{9} + \frac{1600}{9} + \frac{9}{9} + \frac{9}{9} + \frac{1600}{9} - 160 - 1080 = 3600 \]
Combine:
\[ \frac{1050 + 1600 + 9 + 9 + 1600}{9}D - 1240 = 3600 \]
\[ \frac{4200}{9}D = 3600 + 1240 \]
\[ \frac{4200}{9}D = 4840 \]
Multiply both sides by 9:
\[ 4200D = 4840 \times 9 \]
\[ D = \frac{4840 \times 9}{4200} \]
Calculating \(D\):
\[ D = 10.4 \text{ (approximately)} \]

### Step 5: Calculate items sold by store P
Now substitute \(D\) back to find \(A\), \(B\), \(C\), and \(E\):
1. Calculate \(A\):
\[ A = \frac{350}{3}D \]
2. Calculate \(B\):
\[ B = \frac{1600}{9}D \]
3. Calculate \(C\):
\[ C = D - 160 \]
4. Calculate \(E\):
\[ E = \frac{1600}{9}D - 1080 \]

### Step 6: Calculate items sold by store Q
From the problem, we know:
- Total items D sold by store Q is 240 more than store P:
\[ D_Q = D + 240 \]
- Total items B sold by store Q is \(12.5\%\) more than store P:
\[ B_Q = B + 0.125B \]

### Step 7: Calculate total items sold by store Q
Using the ratios given for A, C, and E sold by store Q:
\[ A_Q + C_Q + E_Q = 4800 \]
Where:
- \(A_Q = 26k\)
- \(C_Q = 23k\)
- \(E_Q = 11k\)

### Step 8: Find the percentage difference for item E
Finally, we need to find out what percent more total item E sold by store Q is compared to store P:
\[ \text{Percentage} = \left(\frac{E_Q - E_P}{E_P}\right) \times 100 \]