Five companies P, Q, R, S, and T each manufacture 100,000 bats. The percentage of wooden bats and the ratio of plastic bats labelled Brand A to Brand B for each company are given. Calculate the total number of plastic bats of Brand B manufactured by all companies together.

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1746713137/aptidude_questions/z8hflzi08ygfio51dg8n.png)

Question

Five companies P, Q, R, S, and T each manufacture 100,000 bats. The percentage of wooden bats and the ratio of plastic bats labelled Brand A to Brand B for each company are given. Calculate the total number of plastic bats of Brand B manufactured by all companies together.

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1746713137/aptidude_questions/z8hflzi08ygfio51dg8n.png)

Accepted Answer

Step 1: Calculate the number of plastic bats for each company.
- Total bats per company = 100,000
- Wooden bats % given, so plastic bats % = 100% - Wooden bats %

Company P:
- Wooden bats = 65%, so plastic bats = 35% of 100,000 = 35,000
- Ratio Brand A : Brand B = 3 : 7
- Total parts = 3 + 7 = 10
- Brand B plastic bats = (7/10) * 35,000 = 24,500

Company Q:
- Wooden bats = 70%, plastic bats = 30% of 100,000 = 30,000
- Ratio Brand A : Brand B = 7 : 8
- Total parts = 15
- Brand B plastic bats = (8/15) * 30,000 = 16,000

Company R:
- Wooden bats = 60%, plastic bats = 40% of 100,000 = 40,000
- Ratio Brand A : Brand B = 19 : 6
- Total parts = 25
- Brand B plastic bats = (6/25) * 40,000 = 9,600

Company S:
- Wooden bats = 70%, plastic bats = 30% of 100,000 = 30,000
- Ratio Brand A : Brand B = 7 : 8
- Total parts = 15
- Brand B plastic bats = (8/15) * 30,000 = 16,000

Company T:
- Wooden bats = 50%, plastic bats = 50% of 100,000 = 50,000
- Ratio Brand A : Brand B = 2 : 3
- Total parts = 5
- Brand B plastic bats = (3/5) * 50,000 = 30,000

Step 2: Add all Brand B plastic bats:
24,500 + 16,000 + 9,600 + 16,000 + 30,000 = 96,100

Therefore, the total number of plastic bats of Brand B manufactured by all companies together is 96,100.

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