Correct Answer: 159500

Solution : Given: P is the sum of wooden bats of Brand B manufactured by S and wooden bats of Brand A manufactured by W.
For S,
The percentage of wooden bats = 30%
⇒ The number of wooden bats = 0.30 × 550000 = 165000
The ratio of brand A to Brand B for wooden bats = 8 : 7
The number of brand B wooden bats = $\frac{7}{15}$ × 165000 = 77000
For W,
The percentage of wooden bats = 60%
⇒ The number of wooden bats = 0.60 × 550000 = 330000
The ratio of Brand A to Brand B for wooden bats = 5 : 6
⇒ The number of Brand A wooden bats = $\frac{5}{11}$ × 330000 = 150000
⇒ P = 77000 + 150000 = 227000
Given that Q is the difference between Brand B wooden bats and Brand A wooden bats manufactured by U.
For U,
The percentage of wooden bats = 25%
⇒ The number of wooden bats = 0.25 × 550000 = 137500
⇒ The ratio of Brand A to Brand B for wooden bats = 41 : 14
⇒ The number of Brand A wooden bats = $\frac{41}{55}$ × 137500 = 102500
And, the number of Brand B wooden bats = $\frac{14}{55}$ × 137500 = 35000
⇒ Q = 35000 – 102500 = 67500
Therefore, P – Q = 227000 – 67500 = 159500
Hence, the correct answer is 159500.