Read the given table carefully and answer the following question.

The data below shows the number of watches (Analog + Digital) sold by five shopkeepers on Monday and the ratio of analog to digital watches sold by each shopkeeper on the same day.

| Shopkeepers | Total Sold Watches | Analog : Digital |
|-------------|--------------------|------------------|
| A | 135 | 5 : 4 |
| B | 140 | 9 : 5 |
| C | 180 | 4 : 5 |
| D | 160 | 13 : 19 |
| E | 150 | 7 : 8 |

If only 30\% of the analog watches are sold by shopkeeper B and 75\% of the analog watches remain unsold by shopkeeper A, then what is the total number of analog watches shopkeeper A has as a percentage of the total number of analog watches shopkeeper B has?

Question

Read the given table carefully and answer the following question.

The data below shows the number of watches (Analog + Digital) sold by five shopkeepers on Monday and the ratio of analog to digital watches sold by each shopkeeper on the same day.

| Shopkeepers | Total Sold Watches | Analog : Digital |
|-------------|--------------------|------------------|
| A           | 135                | 5 : 4            |
| B           | 140                | 9 : 5            |
| C           | 180                | 4 : 5            |
| D           | 160                | 13 : 19          |
| E           | 150                | 7 : 8            |

If only 30\% of the analog watches are sold by shopkeeper B and 75\% of the analog watches remain unsold by shopkeeper A, then what is the total number of analog watches shopkeeper A has as a percentage of the total number of analog watches shopkeeper B has?

Accepted Answer

**Solution:**

1. Calculate the number of analog watches sold by shopkeeper A:
   - Total watches sold by A = 135
   - Ratio of analog to digital = 5:4
   - Total parts = 5 + 4 = 9
   - Analog watches sold by A = $ $\frac{5}{9} \times 135 = 75$ $

2. Calculate the total analog watches shopkeeper A has:
   - Given 75\% of analog watches remain unsold by A, so only 25\% are sold.
   - Let total analog watches with A = $ x $
   - Sold analog watches = 30 (since 25\% of $ x $ = 75 sold, this is a contradiction, so re-check)

Correction: The problem states 75\% remain unsold by A, so sold analog watches = 25\% of total analog watches.
   - Sold analog watches by A = 75 (from step 1)
   - So, 25\% of total analog watches = 75
   - $ 0.25x = 75 $  =>  $$ x = \frac{75}{0.25} = 300$ $

3. Calculate the total analog watches shopkeeper B has:
   - Total watches sold by B = 140
   - Ratio of analog to digital = 9:5
   - Total parts = 9 + 5 = 14
   - Analog watches sold by B = $ $\frac{9}{14} \times 140 = 90$ $

4. Given only 30\% of analog watches are sold by B:
   - Let total analog watches with B = $ y $
   - Sold analog watches = 30\% of $ y $ = 90
   - $ 0.3y = 90 $  =>  $$ y = \frac{90}{0.3} = 300$ $

5. Now, find the percentage of total analog watches A has compared to B:
   - $$ \frac{300}{300} \times 100 = 100\%$ $

**Answer:** 100\%

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