In three coloured boxes - Red, Green and Blue, $108$ balls are placed. There are twice as many balls in the green and red boxes combined as there are in the blue box and twice as many in the blue box as there are in the red box. How many balls are there in the green box?

18

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36

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45

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None of these

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Solution

The correct option is C None of these
Let $R$ , $G$ and $B$ represent the number of balls in red, green and blue boxes respectively.
Then,
$R + G + B = 108$ ...(i)
$G + R = 2 B$ ...(ii)
$B = 2 R$ ...(iii)
From (ii) and (iii), we have $G + R = 2 \times 2 R = 4 R$ or $G = 3 R$ .
Putting $G = 3 R$ and $B = 2 R$ in (i), we get:
$R + 3 R + 2 R = 108 \Leftrightarrow 6 R = 108 \Leftrightarrow R = 18$ .
Therefore Number of balls in green box $= G = 3 R = (3 \times 18) = 54$ .

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In three coloured boxes - Red, Green and Blue, 108 balls are placed. There are twice as many balls in the green and red boxes combined as there are in the blue box and twice as many in the blue box as there are in the red box. How many balls are there in the green box?

In three coloured boxes - Red, Green and Blue, $108$ balls are placed. There are twice as many balls in the green and red boxes combined as there are in the blue box and twice as many in the blue box as there are in the red box. How many balls are there in the green box?