Question : Directions: The table given below shows information about bats manufactured by six different companies. Each company manufactures only plastic and wooden bats. Each company labels these bats as Brand A or Brand B. The table shows the number of plastic bats as a percentage of the total bats manufactured by each company. It also shows the ratio of wooden bats labelled A and B. Each company manufactured a total of 550000 bats.

Company	Plastic bats	Brand A: B
R	55%	21 : 4
S	70%	8 : 7
T	45%	6 : 19
U	75%	41 : 14
V	60%	7 : 15
W	40%	5 : 6

P = The sum of wooden bats of Brand B manufactured by S and wooden bats of Brand A manufactured by W.
Q = The difference between Brand B wooden bats and Brand A wooden bats manufactured by U.
What is the value of (P – Q)?

Option 1: 67500

Option 2: 177700

Option 3: 159500

Option 4: 123500

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.