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243 has been divided into three parts such that half of the first part, one-third of the second part and one-fourth of the third part are equal. The largest part is :

243 has been divided into three parts such that half of the first part, one-third of the second part and one-fourth of the third part are equal. The largest part is : Correct Answer 108

Let the three parts be A, B and C
$$\eqalign{ & {\text{Let }}\frac{A}{2} = \frac{B}{3} = \frac{C}{4} = x \cr & {\text{Then, }}A = 2x,B = 3x{\text{ and }}C = 4x \cr & {\text{So, }}A:B:C = 2:3:4 \cr & \therefore {\text{Largest part :}} \cr & = \left( {243 \times \frac{4}{9}} \right) \cr & = 108 \cr} $$

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