$6$ interns and $2$ managers working together can do five times the work that an intern and a manager can do. Calculate the ratio of the working capacities of an intern and a manager?

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Solution

Finding the ratio:
No.of interns $= 6$
No.of managers $= 2$
Let
The work done by an intern $= x$
The work done by the manager $= y$
Therefore,
$\begin{array}{rcl} 6 x + 2 y & = & 5 (x + y) \\ 6 x + 2 y & = & 5 x + 5 y \\ 6 x - 5 x & = & 5 y - 2 y \\ 1 x & = & 3 y \\ \frac{x}{y} & = & \frac{1}{3} \end{array}$
Hence, the ratio of the working capacities of an intern and a manager is $1 : 3$

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6 interns and 2 managers working together can do five times the work that an intern and a manager can do. Calculate the ratio of the working capacities of an intern and a manager?

Finding the ratio:No.of interns=6No.of managers =2LetThe work done by an intern=xThe work done by the manager=yTherefore,6x+2y=5(x+y)6x+2y=5x+5y6x-5x=5y-2y1x=3yxy=13Hence, the ratio of the working capacities of an intern and a manager is 1:3

$6$ interns and $2$ managers working together can do five times the work that an intern and a manager can do. Calculate the ratio of the working capacities of an intern and a manager?