16 horses can haul a load of lumber in 24 minutes. 12 horses

Question

16 horses can haul a load of lumber in 24 minutes. 12 horses started hauling a load and after 14 minutes, 12 mules joined the horses. Will it take less than a quarter-hour for all of them together to finish hauling the load?

(1) Mules work more slowly than horses.
(2) 48 mules can haul the same load of lumber in 16 minutes.

(1) Mules work more slowly than horses.
(2) 48 mules can haul the same load of lumber in 16 minutes.

Bunuel · Accepted Answer

Total work = 16*24 = 384 horse minutes;

Work done by 12 horses in 14 minutes = 12*14 = 168 horse minutes.

Work left = 384 - 168 = 216 horse minutes.

Work done by 12 horses in 15 minutes = 12*15 = 180 horse minutes (work done by 12 horses in quarter-hour).

From (1) we know that 12 mules works slower than 12 horses, so in 15 minutes they can do less than 180 horse minutes work.

Hence, together in 15 minutes they can do less than 360 horse minutes work.

So, in 15 minutes together they can do less as well as more that the amount of the work that is left (216 horse minutes).

That's why (1) is not sufficient.

Hope it's clear.

KarishmaB · Answer

16 horses ........ 24 mins .......... 1 work
12 horses ......... 14 mins .......... ? work

Work done = 1*(14/24)*(12/16) = 7/16 work

Leftover work = 9/16

(1) Mules work more slowly than horses.

Say, consider when mules work almost as efficiently as horses. 12 mules is equivalent to 12 horses in that case.

16 horses ........ 24 mins .......... 1 work
24 horses ......... ?? mins .......... 9/16 work

Time taken = 24*(16/24)*(9/16) = 9 mins
If the mules work slower, time taken will be more till the point when mules work so slowly that they do no work. Since 12 horses take 2 mins to do 1/16th work, they will take 18 mins to complete 9/16 work. So depending on how fast/slow the mules are, time taken could be less/more than 15 mins. Not sufficient

(2) 48 mules can haul the same load of lumber in 16 minutes.
We now know exactly how fast/slow the mules are. So this must be sufficient to say whether time taken was less or more than 15 mins. Sufficient

Answer (B)

jbisht · Answer

let work done by one horse in one min. be 1 unit
so total work = 16*24*1 = 384 units
quarter hour = 15 minutes
work done 12 horses in 15 min = 12*15*1 = 180 units
work left = 384 - 180 = 204 units
works done by 48 maules in 16 min = 384
works done by 12 maules in 1 min = 384x(12/48)x(1/16) = 6 units
so, work left after 15 minutes = 204 - 6 = 198 units
 
Hence, will take more than 15 minutes

MacFauz · Answer

16 horses can haul a load of lumber in 24 minutes.

So, 12 horses can haul the load in 32 minutes
and 24 horses can haul the load in 16 minutes.

So unless the mules are faster than the horses to a certain extent (in this instance they should be mules from Krypton), it is not possible to complete the work in 15 minutes.

1) Sufficient
2)The speed of the mules is given. The statements never contradict each other. So, we do not need to do any calculations to compare it with that of the horses. This statement is sufficient.

Answer is D.

EDIT:

AFTER  seeing the OA, I realize that I could have misunderstood the question. If the question is asking for whether the work can be completed in an additional 15 minutes AFTER the initial 14 minutes, then I guess the working would be different.

12 horses can haul the load in 32 minutes.
So, in 14 minutes they would have hauled  \frac{14}{32}  of the load and the remaining is  \frac{18}{32}  of the load.

24 horses will be able to complete this remaining work in  \frac{18}{32}*16  ie 9 minutes

1) If the mules are only slightly slower than the horses, the work can be finished in under 15 minutes. If the mules are abysmally slower than the horses, it will take more than 15 minutes. Insufficent.

2) The speed of the mules is given and hence whether the work can be finished in under 15 minutes or not can be calculated. Sufficient.

Answer is B.

However, IMHO the presence of this confusion alone makes this question a poor quality one.

mau5 · Answer

Let the work being done by each horse in a givn period of time be called horsepower(HP). Now, given that 16 horses can do some work in 24 minutes. Thus, let this be 16*24 HP. Now, for 12 horses to the same work, we would require,

16*24 = 12*x

or x = 32 minutes.

Now, for 14 minutes, there are 12 horses and they do 12*14 HP work. So the remaining work is (32-14)*12 HP = 18*12 HP

Now, we don't know the relation between the rate of work of mules and that of the horses.

From F.S 1 , we know that mules work at a much smaller rate than the horses.

Scenario 1: Assume(against the option given) that the mules work at the same rate as that of the horses. Thus, 12 mules can be considered as 12 horses. Thus, the time taken for doing 18*12 HP of work :

18*12 = (12+12)*x

or x = 9 minutes.

Thus, as it is given that the rate of work of mules is smaller than that of horses, the time taken will definitely more than 9 minutes.

Assuming that mules work at half the rate of horses,

12 mules = 6 horses.

Thus,  18*12 = (12+6)*x

x = 12 minutes.

Let the rate of work of mules be 1/12th of the horse.

12 mules = 1 horse

Thus,  18*12 = (12+1)*x

x= 16.6 minutes.

Thus, F.S 1 not sufficient.

From F.S 2, you can get the relation between the rates of mule and horse. No need to solve. Sufficient.

B.

tyagigar · Answer

sorry for asking dumb question , i have read the blog but i always get confuse in the realtion thing, for e.g in this case ( how is time taken realted to horses ? it is inversly propotional i.e if more horses are there time taken will be less..............but how is time taken related to work to be done ( do we say if work to be done is less the time taken would be less ? so it is directly propotional but here we have taken work to be done as inversly proptional . i always get confused in this. please help :oops:

KarishmaB · Answer

To make it easier for yourself, you can ignore proportionality. Think in terms of logic. 
You need to find the time taken. Your number of horses has increased from 16 to 24. So now you will need less time to finish the same work. So you multiply your old time with a fraction less than 1 which is 16/24.
Also, the work required to be done has decreased. From 1 to 9/16 (less than 1). So time required to complete the work would be less. This means we will multiply with a fraction less than 1 to make the time less. So you multiply by (9/16)/1 = 9/16.

Note that since horses required and time taken are inversely proportion, you multiplied by 16/24 (first line/second line). Since work to be done and time taken is directly proportional, we multiplied by (9/16)/1 (second line/first line). You will obviously not go wrong if you use proportionality but you might want to just stick to logic to keep it simple.

ClimbingtheladderofS · Answer

Answer D (Not sure if that's right)
The problem tells us that 16 horses need 24 min's to do the job - thus one horse would need 16x24 min's to do the same job alone. 12 horses would need (16x24)/12 = 32 minutes to do the full job. A quarter of an hour is 15 minutes. After 14 minutes 12 mules join the horses. If the mules work faster than the horses it might be possible that they could finish the job in fewer than 15 minutes - but if they work at an equal or slower rate it is not possible (24 mules/horses with the same speed would need 32/2=16 minutes). 
Statement (1) is sufficient as it tells us that the mules work at a slower rate.
Statement (2) tells us that the 12 mules need (48x16)/12 = 64 minutes to do the full job. As 64 minutes > 24 minutes the work rate of the mules is slower than that of the horses. Sufficient

chetan2u · Answer

hi... the point you are missing is that the amount of work left which is not full but 18/32=9/16....
so if both are equally or mules are just slightly slower, they will take 9/16*16=9 mins...
 therefore if they are slightly slow it may take <15 min.. or >15 if very slow...

santorasantu · Answer

I think B is the answer:

Approach is as follows;
from stem

Horses........minutes............total work
16..............24....................16*24 = 384 units
12..............14....................12*14 = 168 units --> work left = 384 - 168 = 216 units of work is left.

from 1: 
mules work slower than horses and 216 units of work is completed by horses and mules together. In 15 mins horses do 12*15 = 180 units of work. Mules do less than 180 units in 15 mins from this statement. together, they can do more than or less than 216 units in 15 mins ---> if mules are too slow.

from 2: 
48 mules can do 384 units of work in 16 mins.
12 mules can do 384 units of work in 16*4 = 64 mins
12 mules can do 216 unis of work in 64*216/384 = 36 mins
12 horses can do 216 units of work in 24*(16/12)*(216/384) = 18 mins (equation is from stem as 16 horses take 24 mins for 384 units of work)

as 12 horses and 12 mules do the work simultaneously: and horses take 18 mins and mules take 36 mins, combined they take (36*18)/(36+18) mins = 12 mins

B

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

The correct response is (B).

The answer is always “yes.” Let’s consider how “big” this lumber-haul job is first. To load the lumber, it took 16 horses x 24 minutes = 384 horse-minutes of work. If mules do it, it takes 48 mules x 16 minutes = 768 mule-minutes of work. Notice that 384 is half of 768! That means that one horse can do the work of two mules.

In 14 minutes, 12 horses will do 12 x 14 = 168 horse-minutes of work. That leaves 384 – 168 = 216 horse-minutes of work left to do.

To complete the job, we have 12 horses and 12 mules. The 12 mules do the work of 6 horses, so 12 horses and 12 mules will do the work at the same rate 18 horses would:

18 horses x ___ minutes =216 horse-minutes of work

216/18 = 12 minutes to complete the remaining work.

If you chose (A), this information is not sufficient. Without knowing how much slower mules work than horses, we cannot answer the question.

If you chose (C), the second statement alone is sufficient.

If you chose (D), the first statement doesn’t tell us anything about the mule’s work-rate.

If you chose (E), the second statement is sufficient because we are given the rates of both animals. You may want to get more practice on challenging work-and-rate word problems to review this difficult concept in more detail.

hycday · Answer

Hi,

Would the following logic be ok during the test or no :

without even computing anything, statement A doesnt give any real info, only 'slower' but it can be much slower, or a lot slower.
statement B does give the rate of the mule, and thus can allow us to make some computation and answer the question (but we wont since we don't need the actual answer).
thus, only statement B is helpful.
done in 20seconds.

would this be correct or can there be a case where only statement A is helpful ? such as a situation where the only fact of knowing that the mule are slower can tell us the answer?

thank you !

chetan2u · Answer

hi, ....
you cannot take this as a routine. It may not have mattered here with the kind of numbers we have...
 but it will not be true if i change only one value in the original question ..

16 horses can haul a load of lumber in 24 minutes. 12 horses started hauling a load and after 14 minutes, 12 mules joined the horses. Will it take less than a quarter-hour for all of them together to finish hauling the load?

(1) Mules work more slowly than horses.
(2) 48 mules can haul the same load of lumber in 16 minutes.

(1) Mules work more slowly than horses.
(2) 48 mules can haul the same load of lumber in 16 minutes.

please find answer for this

devikeerthan · Answer

12 horses started hauling a load and after 14 minutes,  12 mules joined the horses . Will it take less than a quarter-hour for all of them together to finish hauling the load?

Can somebody explain why the underlined portion is used?
work done by all of them together in 15 minutes or work done by horses in 15m+work done by mules in remaining 1 minute after joining? I am not able to get the question

KarishmaB · Answer

You are given:
"16 horses can haul a load of lumber in 24 minutes.
12 horses started hauling a load..."

If fewer horses are actually hauling, will they take more time or less time? More time of course, since they are fewer to do the job. So 12 horses will take more than 24 mins to haul the load.

16 horses do it in 24 mins.
12 horses will do it in 24 * (16/12) = 32 mins

You multiply by 16/12 because you need to increase the time. 16/12 is greater than 1 so it increases the time from 24 mins to 32 mins.

They work for 14 mins and complete 14/32 of the work. They still have 1 - 14/32 = 18/32 of the work leftover. That is when the 12 mules join in.
Now focus on how long it will take 12 horses and 12 mules to do the work.

I have shown the analysis in my post above.

ZaydenBond · Answer

The answer is always “yes.” Let’s consider how “big” this lumber-haul job is first. To load the lumber, it took 16 horses x 24 minutes = 384 horse-minutes of work. If mules do it, it takes 48 mules x 16 minutes = 768 mule-minutes of work. Notice that 384 is half of 768! That means that one horse can do the work of two mules.

This makes no sense what so ever. There are 48 mules doing work in 16 minutes, as opposed to 16 horses doing the work in 24 minutes. How exactly does that mean that one horse does the work of two mules?

KarishmaB · Answer

Think about it this way:

Say 10 children work on painting a fence and finish it off in 10 mins. This means the fence needs 100 child mins to get done. So if 1 child were to paint the entire fence, she would take 100 mins. If 100 children were to work on the fence, they would finish it in 1 min.
Now, say when 4 adults are working on the fence, they take 5 mins to paint it. Hence the same fence takes only 20 adult mins to paint. So if 1 adult were to paint it, he would take 20 mins. 
If 1 child were to paint it, she would take 100 mins but if one adult were to paint it, he would take only 20 mins. So a child takes 5 times as much time as a adult so an adult is equivalent to 5 children. 
Does this help?
The solution uses the same concept.

LogicGuru1 · Answer

(1) Mules work more slowly than horses.
Nothing can be inferred without knowing the actual rate of mules 
INSUFFICIENT

(2) 48 mules can haul the same load of lumber in 16 minutes
The rate of horse is known. the rate of mule is known.
Mixed rates of horse and mules can be find easily using suitable calculations
SUFFICIENT

ANSWER IS B

sayan640 · Answer

KarishmaB   MartyMurray  Can you please elaborate a bit more on the second statement ?

16 horses can haul a load of lumber in 24 minutes. 12 horses

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16 horses can haul a load of lumber in 24 minutes. 12 horses

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