The table below shows the total number of utensils (Glasses and Plates) sold by four shops A, B, C, and D, along with the percentage of glasses sold and the number of plates sold. Some values are missing and need to be calculated.

| Shop | Total Utensils Sold | Percentage of Glasses Sold | Number of Plates Sold |
|-------|---------------------|----------------------------|-----------------------|
| A | 968 | 50\% | ? |
| B | ? | 65\% | ? |
| C | ? | 44\% | 504 |
| D | 900 | ? | ? |

If the total number of utensils sold by shop Y is 200\% more than the number of glasses sold by shop A, and the number of plates sold by Y is $\frac{3}{4}$ of the total utensils sold by Y, then find the sum of the total number of glasses sold by shops Y and C together.

Question

The table below shows the total number of utensils (Glasses and Plates) sold by four shops A, B, C, and D, along with the percentage of glasses sold and the number of plates sold. Some values are missing and need to be calculated.

| Shop | Total Utensils Sold | Percentage of Glasses Sold | Number of Plates Sold |
|-------|---------------------|----------------------------|-----------------------|
| A     | 968                 | 50\%                      | ?                     |
| B     | ?                   | 65\%                      | ?                     |
| C     | ?                   | 44\%                      | 504                   |
| D     | 900                 | ?                          | ?                     |

If the total number of utensils sold by shop Y is 200\% more than the number of glasses sold by shop A, and the number of plates sold by Y is $\frac{3}{4}$ of the total utensils sold by Y, then find the sum of the total number of glasses sold by shops Y and C together.

Accepted Answer

**Solution:**

1. Calculate the number of glasses and plates sold by shop A:
   - Total utensils sold by A = 968
   - Percentage of glasses sold by A = 50\%
   - Number of glasses sold by A = 50\% of 968 = $0.5 \times 968 = 484$
   - Number of plates sold by A = Total utensils - Glasses = 968 - 484 = 484

2. Calculate total utensils sold by shop C:
   - Number of plates sold by C = 504
   - Percentage of glasses sold by C = 44\%
   - Let total utensils sold by C = $x$
   - Plates = Total - Glasses = $x - 0.44x = 0.56x$
   - Given plates = 504, so $0.56x = 504 \Rightarrow x = \frac{504}{0.56} = 900$
   - Number of glasses sold by C = 44\% of 900 = $0.44 \times 900 = 396$

3. Calculate total utensils sold by shop Y:
   - Total utensils sold by Y = 200\% more than glasses sold by A
   - 200\% more means $100\% + 200\% = 300\%$ of glasses sold by A
   - Total utensils sold by Y = $3 \times 484 = 1452$

4. Calculate plates sold by Y:
   - Plates sold by Y = $\frac{3}{4}$ of total utensils sold by Y
   - Plates sold by Y = $\frac{3}{4} \times 1452 = 1089$

5. Calculate glasses sold by Y:
   - Glasses sold by Y = Total utensils - Plates = 1452 - 1089 = 363

6. Find the sum of glasses sold by Y and C:
   - Glasses sold by Y + Glasses sold by C = 363 + 396 = 759

**Answer:** 759

**Note:** The correct option is (d) 759.

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