The table below shows the total number of laptops sold by five different shops along with the ratio of Dell laptops to HP laptops sold by each shop.

| Shops | Total Number of Laptops | Dell : HP |
|-------|------------------------|-----------|
| P | 950 | 11 : 8 |
| Q | 850 | 8 : 9 |
| R | 1080 | 5 : 7 |
| S | 980 | 9 : 5 |
| T | 1150 | 12 : 11 |

The number of HP laptops sold by shop M is 20% more than that sold by shop S. The ratio of Dell to HP laptops sold by shop M is 5 : 7. Find the total number of laptops sold by shop M.

Question

The table below shows the total number of laptops sold by five different shops along with the ratio of Dell laptops to HP laptops sold by each shop.

| Shops | Total Number of Laptops | Dell : HP |
|-------|------------------------|-----------|
| P     | 950                    | 11 : 8    |
| Q     | 850                    | 8 : 9     |
| R     | 1080                   | 5 : 7     |
| S     | 980                    | 9 : 5     |
| T     | 1150                   | 12 : 11   |

The number of HP laptops sold by shop M is 20% more than that sold by shop S. The ratio of Dell to HP laptops sold by shop M is 5 : 7. Find the total number of laptops sold by shop M.

Accepted Answer

**Solution:**

1. From the table, the ratio of Dell to HP laptops sold by shop S is given as 9 : 5, and the total laptops sold by shop S is 980.

2. Let the number of Dell laptops sold by shop S be $9x$ and HP laptops be $5x$.

3. Total laptops sold by shop S:
   $$9x + 5x = 14x = 980$$
   $$x = \frac{980}{14} = 70$$

4. Number of HP laptops sold by shop S:
   $$5x = 5 	imes 70 = 350$$

5. Number of HP laptops sold by shop M is 20% more than that of shop S:
   $$	ext{HP laptops at M} = 350 + 20\% 	ext{ of } 350 = 350 + 70 = 420$$

6. The ratio of Dell to HP laptops sold by shop M is 5 : 7.

7. Let the number of Dell laptops sold by shop M be $5y$ and HP laptops be $7y$.

8. Since HP laptops at M are 420, we have:
   $$7y = 420 \implies y = \frac{420}{7} = 60$$

9. Total laptops sold by shop M:
   $$5y + 7y = 12y = 12 	imes 60 = 720$$

**Answer:** 720

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