Question

Eleanor and Madison completed a work in 6 days. If the efficiency of Eleanor is twice that of Madison, find the part of work done by Madison.

• A. ${\frac{1}{18}}^{th}$ part
• B. ${\frac{1}{3}}^{th}$ part

Answer 1

The correct option is B ${\frac{1}{3}}^{th}$ part

Let the amount of work done by Eleanor be $x$ part in a day.
And, the amount of work done by Madison be $y$ part in a day.

The efficiency of Eleanor is double that of Madison.
$\therefore x=2y...$ (a)

In $6$ days, Eleanor will complete $6x$ part, and Madison will complete $6y$ part.
Also, in $6$ days, the work is completed.
The whole work is represented by $1.$
$\therefore 6x+6y=1...$(b)

Substitute equation (a) in (b).
$6x+6y=1$
$\Rightarrow 6\left(2y\right)+6y=1$
$\Rightarrow 18y=1$
$\Rightarrow y=\frac{1}{18}$
$\therefore$ In a day, Madison comletes ${\frac{1}{18}}^{th}$ part of the work.
$\Rightarrow$ In $6$ days, Madison completes ${\frac{1}{18}}^{th}\times 6={\frac{1}{3}}^{th}$ part of the work.