20 men and 35 women can complete a piece of work in ‘y’ and ‘y – 3’ days respective while 15 men and 20 women can complete same piece of work in ‘x – 4’ and ‘x’ days respectively. If each man are 60% more efficient than each woman, then find difference between x and y.

The correct answer is Option 11.

Step 1: Understand the ratio of efficiency between a man and a woman.

Let the efficiency of a woman be $w$ units per day.

Since each man is 60% more efficient than each woman, the efficiency of a man ($m$) is:

$m=w+0.60w=1.6w=\frac{8}{5}w$

Therefore, the ratio of efficiencies of a man to a woman is:

$\frac{m}{w}=\frac{8}{5}$

Let $m=8$ units/day and $w=5$ units/day.

Step 2: Formulate equations for total work using the given data.

Case 1: 20 men can complete the work in $y$ days, while 35 women can complete the same work in $y-3$ days.

Total Work = Work done by 20 men in $y$ days = $20\times m\times y$

Total Work = Work done by 35 women in $y-3$ days = $35\times w\times (y-3)$

Equating the total work expressions:

$20\times 8\times y=35\times 5\times (y-3)$

$160y=175(y-3)$

$160y=175y-525$

$15y=525$

$y=35$

Step 3: Calculate the value of $x$.

Case 2: 15 men can complete the work in $x-4$ days, while 20 women can complete the same work in $x$ days.

Total Work = Work done by 15 men in $x-4$ days = $15\times m\times (x-4)$

Total Work = Work done by 20 women in $x$ days = $20\times w\times x$

Equating these two total work expressions:

$15\times 8\times (x-4)=20\times 5\times x$

$120(x-4)=100x$

$120x-480=100x$

$20x=480$

$x=24$

Step 4: Find the difference between $y$ and $x$.

Difference = $y-x=35-24=11$

Thus, the difference between $x$ and $y$ is 11.