Question

Divide 243 in three parts such that half of part ,one-third of second part and one forth of thrid part are equal.

Answer 1

Let the numbers be x, y, and z
$So \\ \frac{1}{2} x = \frac{1}{3} y = \frac{1}{4} z = k \\ x = 2k \: \\ y = 3k \\ z = 4k \\ and \\ x+y+z = 243 \\ 2k+3k+4k = 243 \\ 9k = 243 \\ k = 27 \\ \: now \\ x = 2k = 2 \times 27 = 54 \\ y = 3k = 3 \times 27 = 81 \\ z \: = 4k = 4 \times 27 = 108$

Answer 2

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