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

Taking all 6 companies together, how many wooden bats of Brand A have been produced?

Option 1: 691000

Option 2: 724000

Option 3: 683000

Option 4: 716000

Correct Answer: 691000

Solution : For R,
The percentage of wooden bats = 45%
$\therefore$ The number of wooden bats = 0.45 × 550000 = 247500
The ratio of Brand A to Brand B for wooden bats = 21 : 4
$\therefore$ The number of Brand A wooden bats = $\frac{21}{25}$ × 247500 = 207900
For S,
The percentage of wooden bats = 30%
$\therefore$ The number of wooden bats = 0.30 × 550000 = 165000
The ratio of Brand A to Brand B for wooden bats = 8 : 7
$\therefore$ The number of Brand A wooden bats = $\frac{8}{15}$ × 165000 = 88000
For T,
The percentage of wooden bats = 55%
$\therefore$ The number of wooden bats = 0.55 × 550000 = 302500
The ratio of Brand A to Brand B for wooden bats = 6 : 19
$\therefore$ The number of Brand A wooden bats = $\frac{6}{25}$ × 302500 = 72600
For U,
The percentage of wooden bats = 25%
$\therefore$ The number of wooden bats = 0.25×550000 = 137500
The ratio of Brand A to Brand B for wooden bats = 41 : 14
$\therefore$ The number of Brand A wooden bats = $\frac{41}{55}$ × 137500 = 102500
For V,
The percentage of wooden bats = 40%
$\therefore$ The number of wooden bats = 0.40 × 550000 = 220000
The ratio of Brand A to Brand B for wooden bats = 7: 15
$\therefore$ The number of Brand A wooden bats = $\frac{7}{22}$ × 220000 = 70000
For W,
The percentage of wooden bats = 60%
$\therefore$ The number of wooden bats = 0.60 × 550000 = 330000
The ratio of Brand A to Brand B for wooden bats = 5 : 6
$\therefore$ The number of Brand A wooden bats = $\frac{5}{11}$ × 330000 = 150000
$\therefore$ The total number of wooden bats of Brand A produced by all six companies
= 207900 + 88000 + 72600 + 102500 + 70000 + 150000 = 691000
Hence, the correct answer is 691000.