X cornflake is 55% fibre and Y cornflake is 70% fibre. Sharad combine

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:



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.