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 given 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. Study the table carefully and answer the question that follows. 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
96,100
Step 1: Calculate the total number of plastic bats for each company
Plastic bats = Total bats − Wooden bats
For each company, the calculation is as follows:
- P: 1,00,000 − 65% of 1,00,000 = 1,00,000 − 65,000 = 35,000
- Q: 1,00,000 − 70% of 1,00,000 = 1,00,000 − 70,000 = 30,000
- R: 1,00,000 − 60% of 1,00,000 = 1,00,000 − 60,000 = 40,000
- S: 1,00,000 − 70% of 1,00,000 = 1,00,000 − 70,000 = 30,000
- T: 1,00,000 − 50% of 1,00,000 = 1,00,000 − 50,000 = 50,000
Step 2: Calculate the number of plastic bats labelled as Brand B
Brand B bats = Total plastic bats × (Ratio for Brand B)
For each company, the calculation is as follows:
- P: Brand B = 35,000 × 7 ÷ (3 + 7) = 35,000 × 7 ÷ 10 = 24,500
- Q: Brand B = 30,000 × 8 ÷ (7 + 8) = 30,000 × 8 ÷ 15 = 16,000
- R: Brand B = 40,000 × 6 ÷ (19 + 6) = 40,000 × 6 ÷ 25 = 9,600
- S: Brand B = 30,000 × 8 ÷ (7 + 8) = 30,000 × 8 ÷ 15 = 16,000
- T: Brand B = 50,000 × 3 ÷ (2 + 3) = 50,000 × 3 ÷ 5 = 30,000
Step 3: Total number of Brand B bats
Total = 24,500 + 16,000 + 9,600 + 16,000 + 30,000 = 96,100
Thus, the correct answer is (2) 96,100.
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