A chef can bake a certain number of cakes in a given amount of time. I

Question

A chef can bake a certain number of cakes in a given amount of time. An assistant can bake thrice as many pies in twice the time. It takes twice as long to bake a cake than it does a pie. If, together, they can bake 20 cakes and 30 pies in 4 hours, how many pies can the chef alone bake in an hour?

(A) 12
(B) 15
(C) 7.5
(D) 10
(E) 12.5

(A) 12
(B) 15
(C) 7.5
(D) 10
(E) 12.5

yashikaaggarwal · Accepted Answer

A chef can bake a certain number of cakes in a given amount of time. 
let chef bake X cakes in Y hour

In twice that time, an assistant can bake thrice the number of pies as the chef can bake cakes in the given amount of time.
assistant bake 3x pie in 2Y hours
1.5x in Y hour
(the assistant bakes 1.5 times more pies than chef bakes cake in a given time)

For both the chef and the assistant, working at their respective efficiencies, it takes twice as long to bake a cake than it does a pie. 
cake making time = 2 pies making time

If, together, they can bake 20 cakes and 30 pies in 4 hours,
(30 is 1.5 time more than 20, satisfying constraint)

the chef baked 20 cakes in 4 hours
5 cakes in an hour
and one cake baking time = 2 pie making time
5 cake baking time = 2*5 = 10 pie making time.

The chef can make 10 pies in an hour.
Answer is D

IanStewart · Answer

If a cake takes twice as long as a pie, then each cake is like 2 pies. So they can make 70 pies together in 4 hours.

The second sentence of the question isn't in English, but I think they mean to say that the number of pies the assistant can make in 2 hours is 3 times the number of cakes the chef can make in 1 hour. If c is the number of cakes the chef makes in an hour, then 2c is the number the chef makes in 2 hours, and since a cake is like 2 pies, the chef makes 4p pies in 2 hours. The assistant makes 3p pies in 2 hours. So in a fixed amount of time, the work done by the chef and by the assistant is in a 4 to 3 ratio, and if they can make 70 pies in 4 hours together, the chef must be making 40 of those pies, and thus makes 10 pies per hour.

The question is not well-written - what is the source?

effatara · Answer

The question has been edited. Hope it is clearer now.

Thelegend2631 · Answer

Hi Ian ! Isn't the info about the Assistant - pie unnecessary. it basically says cakes take twice as much time. so he makes 5cakes / Hour, since pie takes half as long, he would make 10 pies in an hour. Straight ! Or... AM I MISSING SOMETHING ?

indrajeet999 · Answer

Let say x are the cake's baked in given time 
Therefore 1/X will be the cake's baked in (per given time)
For Pie , It should be (3)*(1/x) / 2 Pies in (per given time) as per the question

Now applying (Total work) / (Total per unit work) = Total time taken,

(50) / (1/x +3/2x) = 4

X turn's out to be 1/5

As mentioned above , 1/x is the cakes baked per given time, substituting 1/5 in place of x , we get 5 cakes per given time

As per the question , It takes twice as long to bake a cake than it does a pie,
Therefore 10 will be the pies baked per given time

Please let me know if this approach is correct.
Thanx in advance

Fdambro294 · Answer

“Chef can bake a certain number of cakes in a given amount of time”

Let’s do everything on a per hour basis. Assume he can bake X cakes per hour and he spends T hours working

Chef: ———- T hours ———-> X cakes

“Assistant can bake 3 times as many pies as the chef can bake cakes in twice the time

Asst. ————— 2T hours ———> 3X pies

“It takes twice as long to make a cake than it does to make a pie”

Further, the question asks us how many PIES the Chef can bake in 1 hour

If it takes twice as long to make 1 cake than it does 1 pie ——-> than for every 1 cake made during a constant time, 2 PIES can be made during that same constant time

So, the chef can make TWICE as many pies in the same time he makes his cakes

Chef: —————> T hours ———-> 2X pies

Furthermore, together they make 20 cakes and 30 pies in 4 hours

The work/manpower put into making 20 cakes = the work/manpower put into making 40 pies

Rephrased: we can say they make 70 pies in 4 hours

(rate of chef) + (rate of assistant) = (70 pies) / (4 hours)

Rate of chef from above = (2X pies) / (T hours) = what we are asked to calculate = (2X / T) = ?

Rate of assistant from above = (3X pies) / (2T hours)

Add the Rates:

(2X / T) + (3X / 2T) = (70 / 4)

(7X / 2T) = (70 / 4)

(X / T) = (10 / 2) = 5 pies per hour

The chef’s Rate of pies per hour was: (2X / T) = (2 * 5) =

10 pies per hour

Posted from my mobile device

varshas044 · Answer

A tricky problem indeed, but let’s work backwards

We are given that chef bakes 20 cakes in 4 hour ---------- 5 cakes in 1 hour

Asst bakes 30 pies in 4 hours ------------ 7.5 pies in 1 hour

Given 
Time for baking cake = 2 x time for baking pie 
Time for baking a pie = ½ x time for baking a cake

It is essentially saying that if we bake pies instead of cakes we can do it twice as fast

If the chef is baking 5 cakes in an hour, since the time for baking pies in half, he WILL BE ABLE TO DO DOUBLE THE WORK 
Hence chef will be able to bake 10 pies in an hour. 
 
Answer – D

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A chef can bake a certain number of cakes in a given amount of time. I

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