The question gives you two different equations as well as two factors:

Let's say kate charged x hours and Mark y hours.

The first equation tells us that pat + kate + mark charged 162 hours together, and that pat charged twice as much as kate, so the equation is:
2x + x + y = 162


the second equation tells us that Mark charged three times as much as Pat, or:
3 * 2x = y

substitue 6x with y in the first equation to get:
2x + x + 6x = 162
x = 18

so Kate charged 18 hours, Mark charged six times as much, or 108.
108 - 18 = 90 , [D] is the answer.

well done! thanks, i realize how close i was, next time around I should stop confusing myself when translating the problem into equations as the math itself is simple. when pressured, the translation part can be horrible for me.

Hello guys,

I'm reopening this thread.

My approach is lets take time taken by Pat=X
Therefore kate=X/2 and Mark=3X

X+X/2+3x=162.

and X=27

So I get the 36 as answer.

I'm not able to understand what is wrong in my approach.

Could anybody help me here.

Thanks,
Shobha

getso wrote: X+X/2+3x=162.

and X=27

So I get the 36 as answer.

Your method is right but your calculation is wrong.

x + x/2 + 3x = 162

2*x + x + 2*3x = 2*162

9x = 324

x = 36

So, Mark is charged 3*36 = 108
Kate is charged 36/2 = 18

Mark - Kate = 108 - 18 = 90 (D)

x + x/2 + 3x = 162

i.e. 4x + x/2 = 162
==> 9x/2 = 162
9x = 324 i.e. x = 36

x = p's time which is twice of K so k = 18 and M = 3x so 3*36=108
and M-K= 108-18 = 90.

HTH

Ya that was a calculation mistake....

@papagust: Thanks for pointing it out.

Regards,
Shobha

p/a=2/1
p/m=1/3


pm
2:1:-
2:-:6

pm
2:1:6

2x+x+6x=162
x=18

(6-1)*18=90