Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?
5 : 7 : 8
20 : 49 : 64
38 : 28 : 21
None of these
Explanation:
Let their investments be Rs. $ x $ for 14 months, Rs. $ y $ for 8 months and Rs. $ z $ for 7 months respectively.
Then, 14$ x $ : 8$ y $ : 7$ z $ = 5 : 7 : 8.
Now,$ \dfrac{14x}{8y} $=$ \dfrac{5}{7} $ $\Leftrightarrow $ 98$ x $ = 40$ y $ $\Leftrightarrow$ $ y $ =$ \dfrac{49}{20} x $
And,$ \dfrac{14x}{7z} $=$ \dfrac{5}{8} $ $\Leftrightarrow$ 112$ x $ = 35$ z $ $\Leftrightarrow$ $ z $ =$ \dfrac{112}{35} x $ =$ \dfrac{16}{5} x $.
$\therefore x $ : $ y $ : $ z $ = $ x $ :$ \dfrac{49}{20} x $:$ \dfrac{16}{5} x $= 20 : 49 : 64.