Below colored part is what I was missing.
I thought the statement saying - Franco and Pierre working together decorated 20 cakes rather than the complete job is to decorate 20 cakes.
so as per my equation - Leftover work = 1-z/x which was making no sense.
Thanks again. Appreciate your efforts
imhimanshu wrote:
Hi Bunuel,
Request you to provide me your approach. I couldn't solve it.
Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry chef Franco takes y hours to decorate a wedding cake. If Pierre works alone for z hours and is then joined by Franco until 20 cakes are decorated, for how long did the two pastry chef's work together.
1- 20xz-y/(x+y)
2- y+z/(20xz)
3- 20x(y-z)/(x+y)
4- 20xy-z/(x+y)
5- y(20x-z)/(x+y)
I usually solve such questions by using below approach-
(Workdone by entity A)/(Time taken by entity a) + (Workdone by entity b)/(time taken by entity b) = (Work done together)/(Time taken together)
However, I was unable to apply the above framework on this question. Please help me out.
Thanks
Let me give you my approach to these problems (I am sure Bunuel will give his solution too so you needn't be disappointed
)
I like to solve questions with variables by plugging in values:
Say x = 1 (Pierre decorates 1 cake in 1 hr), y = 2 (Franco decorates 1 cake in 2 hrs)
Together, they decorate 1 cake in 1/(1+1/2) = 2/3 hrs
Say Pierre decorates 17 cakes in 17 hrs and then Franco joins in and they decorate the remaining 3 cakes in 2 hrs (For 1 cake, they take 2/3 hrs so for 3 cakes, they will take 3*(2/3) = 2 hrs)
Now just plug these values x = 1, y = 2 and z = 17 in the options and whichever option gives you 2, that should be the answer.
Only option (E) gives you 2 so it should be your answer.
Note: While you are trying the options, you can quickly see that numerator will not be divisible by denominator or one of them is way too big so you don't have to perform the complete calculation since you are looking for 2 as your answer. e.g.
you try option (A) 20xz-y/(x+y) = [20*1*17 - 2]/3 (numerator is way too big so not possible)
Option (B) y+z/(20xz) = (2+17)/20*1*17 (denominator is way too big)
You can also use algebra:
Remember two things:
1. Work = Rate*Time
2. We add rates.
Their combined rate of work = 1/x + 1/y
Pierre does some work on his own. Work done by Pierre alone = Pierre's rate * Time = (1/x)*z
Leftover work = 20 - z/xTime taken to complete leftover work together = Work/Rate = (20 - z/x)/(1/x + 1/y) = y(20x - z)/(x+y)
70% (02:15) correct 
