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 |
X = Average of plastic bats manufactured by V, U, and T.
Y = Wooden bats of Brand A manufactured by V.
What is the value (X – Y)?
Option 1: 197600
Option 2: 432890
Option 3: 260000
Option 4: 293300
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Correct Answer: 260000
Solution :
X is the average of plastic bats manufactured by V, U, and T.
For V, the percentage of plastic bats is 60%.
The number of plastic bats = 0.60 × 550000 = 330000
For U, the percentage of plastic bats is 75%.
The number of plastic bats = 0.75 × 550000 = 412500
For T, the percentage of plastic bats is 45%.
The number of plastic bats = 0.45 × 550000 = 247500
$\therefore$ X = $\frac{330000 + 412500 + 247500}{3}$ = 330000
Y is the number of wooden bats of Brand A manufactured by V.
For V, the percentage of wooden bats = 100% – 60% = 40%
The number of wooden bats = 0.40 × 550000 = 220000
Since the ratio of Brand A to Brand B for wooden bats is 7 : 15.
So, the number of Brand A wooden bats = $\frac{7}{22}$ × 220000 = 70000
$\therefore$ Y = 70000
⇒ X – Y = 330000 – 70000 = 260000
Hence, the correct answer is 260000.
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