Five different companies, P, Q, R, S, and T, manufacture plastic and wooden bats. These bats are labelled as Brand A or Brand B. The table shows the number of wooden bats as a percentage of the total bats manufactured by each company. It also shows the ratio of plastic bats labelled as Brand A to Brand B. Each company manufactures 1,00,000 bats. Taking all companies together, how many plastic bats of Brand B have been manufactured?

Company	Wooden bats (%)	Brand A : Brand B
P	65%	3:7
Q	70%	7:8
R	60%	19:6
S	70%	7:8
T	50%	2:3

Total bats manufactured by each company = 1,00,000

Wooden bats as a percentage for each company is provided.

The ratio of plastic bats labelled as Brand A to Brand B for each company is provided.

Number of plastic bats = Total bats - Number of wooden bats

Number of Brand B plastic bats = (Ratio of Brand B / Total ratio) × Number of plastic bats

For Company P

Wooden bats = 65% of 1,00,000 = 65,000

Plastic bats = 1,00,000−65,000 = 35,000

Brand A : Brand B = 3:7 → Fraction of Brand B = $$\frac{7}{3+7}$$​ = $$\frac{7}{10}$$​ 

Plastic bats of Brand B = 35,000 × $$\frac{7}{10}$$​ = 24,500

For Company Q

Wooden bats = 70% of 1,00,000 = 70,000

Plastic bats = 1,00,000−70,000=30,000

Brand A : Brand B = 7:8 → Fraction of Brand B =$$\frac{8}{7+8}$$​ = $$\frac{8}{15}​$$​​

Plastic bats of Brand B = $$30,000 \times \frac{8}{15}$$​ = 16,000

For Company R

Wooden bats = 60% of 1,00,000 = 60,000

Plastic bats = 1,00,000 − 60,000 = 40,000

Brand A : Brand B = 19:6 → Fraction of Brand B = $$\frac{6}{19+6}$$​ = $$\frac{6}{25}$$​​

Plastic bats of Brand B = $$40,000 \times \frac{6}{25}$$​ = 9,600

For Company S

Wooden bats = 70% of 1,00,000 = 70,000

Plastic bats = 1,00,000−70,000 = 30,000

Brand A : Brand B = 7:8 → Fraction of Brand B = $$\frac{8}{7+8}$$​= $$\frac{8}{15}$$​​

Plastic bats of Brand B = $$30,000 \times \frac{8}{15}$$​ = 16,000

For Company T

Wooden bats = 50% of 1,00,000 = 50,000

Plastic bats = 1,00,000 − 50,000 = 50,000

Brand A : Brand B = 2:3 → Fraction of Brand B = $$\frac{3}{2+3} = \frac{3}{5}$$​​

Plastic bats of Brand B = $$50,000 \times \frac{3}{5} = 30,000$$​​

Total plastic bats of Brand B:

24,500 + 16,000 + 9,600 + 16,000 + 30,000 = 96,100

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