A) 85
B) 64
C) 72
D) 40
Correct Answer: C
Solution :
Let the number be x. Then, One-third of \[x=\frac{x}{3}\], Quarter of \[x=\frac{x}{4}\] One-twelfth of \[x=\frac{x}{12}\] Average of third, quarter and one-twelfth of x = \[\frac{\left( \frac{x}{3}+\frac{x}{4}+\frac{x}{12} \right)}{3}=\frac{1}{3}\left( \frac{x}{3}+\frac{x}{4}+\frac{x}{12} \right)\] According to question, we have \[\therefore x=\frac{1}{3}\left( \frac{x}{3}+\frac{x}{4}+\frac{x}{12} \right)+56\] \[\Rightarrow x=\frac{x}{9}+\frac{x}{12}+\frac{x}{36}+56\] \[\Rightarrow x-\frac{x}{9}-\frac{x}{12}-\frac{x}{36}=56\] \[\Rightarrow 36x-4x-3x-x=36\times 56\] \[\Rightarrow 28x=36\times 56\Rightarrow x=\frac{36\times 56}{28}\] \[\Rightarrow x=72\] Hence, the number is \[72\].
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