Question

3 brothers have 58 years in total. How old is the youngest brother if 3/4 of his age equals to 2/3 of middle brother's age and 3/4 of youngest brother's age equals to half of oldest brother's age?​

Answer 1

Step-by-step explanation:

Let O represents older brother

M represents middle brother

& Y represents younger brother.

Therefore, according to the given condition:

$\frac{3}{4} y = \frac{2}{3} m = \frac{1}{2} o \\ \\ \therefore \: \frac{3}{4} y = \frac{2}{3} m \\ \implies \: m = \frac{3}{2} \times \frac{3}{4} y = \frac{9}{8} y \\ \\ next \: \: \frac{3}{4} y = \frac{1}{2} o \\ \implies \: o = \frac{2}{1} \times \frac{3}{4} y = \frac{3}{2} y \\ \\ \because \: o + m + y = 58 \\ \\ \therefore \: \frac{3}{2} y + \frac{9}{8} y + y = 58 \\ \\ \therefore \: \frac{12}{8} y + \frac{9}{8} y + \frac{8}{8} y = 58 \\ \\ \therefore \: \frac{29}{8} y = 58 \\ \\ \therefore \: y = 58 \times \frac{8}{29} \\ \\ \therefore \: y = 2 \times 8 \\ \\ \therefore \: y = 16 \: years$

Thus youngest brother is 16 years old.