Solution: We can use either the weighted average or the allegation method to solve this question.
Weighted average method:We know the resultant % \(= x = 65\)%
We know % of fibre in \(X = x1 = 55\)%
We know the % of fibre in \( Y = x2 = 70\)%
We know the weighted average formula: \(x = \frac{(w1x1+w2x2)}{(w1+w2)}\)
So, \(65 = \frac{(55w1 + 70w2)}{(w1 + w2)}\)
\(⇒ 65w1 + 65w2 = 55w1 + 70w2 \)
\(⇒ 10w1 = 5w2\)
\(⇒ \frac{w1}{w2} = \frac{5}{10}\)
\(⇒ \frac{w1}{w2} = \frac{1}{2}\)
So the ratio of weights in which X and Y is added is \(1 : 2\)
So the amount of X in \(120\)gm of cereal \(= \frac{1}{3}\times 120 = 40\)gms
Allegation method: Attachment:
alle.png [ 2.03 KiB | Viewed 2615 times ]
So the ratio of weights in which X and Y is added is \(5 : 10 = 1 : 2\)
So the amount of X in \(120\)gm of cereal \(= \frac{1}{3}\times 120 = 40\)gms
Hence the right answer is
Option B.