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1. 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 :

A. 74

B. 86

C. 92

D. 108

Solution:

Let the three parts be A, B and C

\begin{aligned} Let \frac{A}{2} = \frac{B}{3} = \frac{C}{4} = x \\ Then, A = 2 x, B = 3 x and C = 4 x \\ So, A : B : C = 2 : 3 : 4 \\ ∴ Largest part : \\ = (243 \times \frac{4}{9}) \\ = 108 \end{aligned}

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