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### Question

The average weight of the students of a class is 4 Kg, and the average weight of the students of another class is 14 Kg. What is the ratio of the number of students in the two classes if the combined average weight is 13 Kg?

**A**

${1/9}$.

**B**

$1{1/4}$.

**C**

$1{8/11}$.

**D**

$2{6/11}$.

**Soln.**

**Ans: a**

If a sample n_{1} has a weighted average of A_{1}, and another sample n_{2} has a weighted average of A_{2}, then the weighted average, A,of the combined samples is determined by the alligation formula as: n_{1}(A - A_{1}) = n_{2}(A_{2} - A). So the ratio is ${A_2 - A}/{A - A_1 }$. Putting A_{2} = 14, A_{1} = 4, and A = 13, we have ${14 - 13}/{13 - 4 }$, from where we get the ratio as ${1/9}$.