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 |
$N$ = Wooden bats of Brand B manufactured by U
$M$ = Total wooden bats manufactured by R and W together.
What is the value of $\frac{N}{M}$?
Option 1: 0.043
Option 2: 0.061
Option 3: 0.125
Option 4: 0.087
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Correct Answer: 0.061
Solution :
Given that,
N = Wooden bats of Brand B manufactured by U
For company U,
The total number of bats is 550000, and 75% are plastic bats.
The number of wooden bats is 25%.
So, the number of wooden bats = 550000 × $\frac{25}{100}$ = 137500
The ratio of Brand A to Brand B wooden bats for company U is 41 : 14.
So, N = 137500 × $\frac{14}{55}$ = 35000
M = Total wooden bats manufactured by R and W together
For company R, 55% of the bats are plastic, and 45% are wooden.
$\therefore$ Number of wooden bats = 550000 × $\frac{45}{100}$ = 247500
For company W, 40% of the bats are plastic and 60% are wooden.
$\therefore$ Number of wooden bats = 550000 × $\frac{60}{100}$ = 330000
So, M = 247500 + 330000 = 577500
⇒ $\frac{N}{M} = \frac{35000}{577500}$ = 0.061
Hence, the correct answer is 0.061.
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