Question

in order to reach the cave?
There are 27 red and 13 blue coloured balls in a bag. The ratio of the weight of one red ball to the weight
of one blue ball is 9:4. The total weight of all the balls is 65 kg. Find the percentage of the weight of
blue balls in the bag (correct to 2 decimal place).
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Answer 1

Answer:

There are 27 red and 13 blue balls in a bag. The ratio of the weight of one red and one blue ball is 9:4. The total weight of all the balls is 65 kg. What is the percentage of the weight of the blue balls in the bag?

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Let R = 1 red ball, B = 1 blue ball.

If the weight ratio of R/B = 9/4, the percentage of the B balls’ weight in the bag = (13*4)/[(27*9)+(13*4)] = .17627118…~ 17.6%.

Edit: The foregoing can also be arrived at using a little more detail as follows.

Note that 1R is 9/4 times the weight of 1B and conversely 1B is 4/9 the weight of 1R. We can therefore say 27R + 13*(4/9)*R = (32.777777…)R = 65 kg and the weight of 1R = 65/(32.7777777…) = (1.9830508…) kg.

We can then also say that 27*(9/4)*B + 13B = (73.75)B = 65 kg and the weight of 1B = 65/( 73.75) = (.88135593…) kg.

Weight of 13B thus = 13*(.88135593…) kg = (11.457627…) kg.

Percent weight of 13B, relative to 27R + 13B = [(11.457627…)/65]*100 ~ 17.6%