If $$\mid x - 6 \mid = 5$$ and $$\mid 3y - 12 \mid = 6$$ then the maximum value of $$\frac{x}{y} =$$

Solution

$$\mid x - 6 \mid = 5$$    |x-6|=5

if x-6 > 0 ; x>6

so the mod function will become, x-6 = 5

x=11......x max.

If x-6 < 0 ; x<6

so the mod function will become, -(x-6) = 5

6 -x = 5

x=6-5 =1  .....x min

Similarly for y

$$\mid 3y - 12 \mid = 6$$    |3y-12|= 6

If 3y-12 < 0, y < 4

so the mod function will become, - (3y-12) = 6

12 -3y = 6 ; y =2 ........y min.

If 3y-12 > 0, y > 4

so the mod function will become, (3y-12) = 6

3y = 12+6 = 18

y = 6 .......y max

For,maximum value of $$\frac{x}{y} =$$ Numerator (x) should be maximum and denominator (y) should be minimum.

$$\frac{x\ \left(\max\right)}{y\left(\min\right)}\ =\ \frac{11}{2\ }$$ Answer