Question

A legacy of $6800 has to be divided among three brothers in the ratio 1/9: 1/3: 1/2. How much each brother will receive?.

Answer 1

Answer

${\sf \dashrightarrow \dfrac{1}{9} : \dfrac{1}{3} : \dfrac{1}{2} = 6800}$

${\sf \dashrightarrow \dfrac{1}{9}x + \dfrac{1}{3}x + \dfrac{1}{2}x = 6800}$

${\sf \dashrightarrow \dfrac{2}{18}x + \dfrac{6}{18}x + \dfrac{9}{18}x = 6800}$

${\sf \dashrightarrow \dfrac{2 + 6 + 9}{18}x = 6800}$

${\sf \dashrightarrow \dfrac{17}{18}x = 6800}$

${\sf \dashrightarrow x = 6800 \div \dfrac{17}{18}}$

${\sf \dashrightarrow x = \dfrac{6800}{1} \times \dfrac{18}{17}}$

${\sf \dashrightarrow x = \dfrac{6800 \times 18}{17} = \dfrac{122400}{17}}$

${\sf \dashrightarrow x = \cancel \dfrac{122400}{17} = 7200}$

Now, let's find out that how much each brother will receive.

Shares of first brother :

${\sf \dashrightarrow \dfrac{1}{9}x = \dfrac{1}{9} \times 7200}$

${\sf \dashrightarrow \cancel \dfrac{7200}{9} = 800}$

Shares of second brother :

${\sf \dashrightarrow \dfrac{1}{3}x : \dfrac{1}{3} \times 7200}$

${\sf \dashrightarrow \dfrac{7200}{3} = 2400}$

Shares of third brother :

${\sf \dashrightarrow \dfrac{1}{2}x = \dfrac{1}{2} \times 7200}$

${\sf \dashrightarrow \dfrac{7200}{2} = 3600}$

Hence, the first, second and third brothers get 800, 2400 and 3600 part of legacy respectively.