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28 May 2024, 03:47
Kudos
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sayan640
We can solve it but it will take unnecessary time. Learn to identify when you will get the answer without the need to calculate.
Statement 2 will give us the equivalence between horses and mules.
48 mules can haul the same load of lumber in 16 minutes.
16 horses can haul a load of lumber in 24 minutes. So to haul it in 16 mins, we will need 16 * 3/2 = 24 horses.
Hence 48 mules is equivalent to 24 horses i.e. 1 horse is equivalent to 2 mules.
16 horses can haul a load of lumber in 24 minutes.
So 12 horses will take 24 * 16/12 = 32 mins. They work for 14 mins to complete 14/32 of the work. We are left with 18/32 of the work.
Then 12 mules i.e. 6 horses join in and we have 18 horses. 18 horses will take 32 * 2/3 = 64/3 mins to complete the entire work.
To complete 18/32 of work, they need (18/32) / (3/64) = 12 mins. So they will finish hauling the load in less than a quarter hour.
Statement 2 is sufficient alone. Note that I work with fractions here to avoid the big calculations. You can also use the method of "horse minutes of work" described above in the official solution.
18 Sep 2025, 20:08
Kudos
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People X Rate X Time = Work Done......
16 X R X 24 = 1
The rate of 1 Horse is 1/(24 x 16)
The rate of 12 Horses is 12/(24 x 16) Means It's 1/32
Now..Work Begins
The 12 Horses do the job for 14 Minutes Means they complete 14/32 Part of the Job....
How much is remaining? 18/32 Part of the Job (I know Fractions can be confusing)
Job Remaining 18/32
Current Manpower(Or Horsepower) is 1/32
12 Mules join....
Can the remaining work be done in next 15 minute?
Statement 1..Mules are slower.....
So slow that they will do ......0.0000000000000000000000001 Part of work ...Almost negligible....
So Will it take more than 15 minute to do 18/32 Part of the work? Yes..Since the rate of 12 horses is 1/32..So it will take nearly (not exactly, but a little less) 18 Minutes....
But..What if the rate of Mules is nearly the same as horse (not exactly the same).. Lets say 12 mules have the rate of a little less than 1/32...
Now in the next 14 minutes...Horse will do 14/32 of the job...and mules will also do 13/32 of the job...Means 30/32 of the job....Do we have the job remaining? No!
They had to do 18/32 in less than 15 mins..they did 27/32 in less than 15 mins....
Hence Statement 1 is not sufficient..
(2) 48 mules can haul the same load of lumber in 16 minutes.
Means 48 Mules do 1/16th of the work in 1 minute
1 Mule does ...1/(16 x 48)th part of work in 1 minute
12 mules will do 12/(16 x 48) parts Means 1/64th part in 1 minute...
They are just half as fast as the horses
So for the next 14 minutes
Horses will do 14/32 Part of the work and Mules will do 14/64 Part of the work means 7/32 Part of the work...
Together they have done 21/32 Part of the work...we just needed 18/32 Part of the work in less than 15 minutes...Hence Statement 2 is sufficient ..answer B...
P.S..This was good for practice, but I don't think a question would come that would require so many calculations etc.
16 X R X 24 = 1
The rate of 1 Horse is 1/(24 x 16)
The rate of 12 Horses is 12/(24 x 16) Means It's 1/32
Now..Work Begins
The 12 Horses do the job for 14 Minutes Means they complete 14/32 Part of the Job....
How much is remaining? 18/32 Part of the Job (I know Fractions can be confusing)
Job Remaining 18/32
Current Manpower(Or Horsepower) is 1/32
12 Mules join....
Can the remaining work be done in next 15 minute?
Statement 1..Mules are slower.....
So slow that they will do ......0.0000000000000000000000001 Part of work ...Almost negligible....
So Will it take more than 15 minute to do 18/32 Part of the work? Yes..Since the rate of 12 horses is 1/32..So it will take nearly (not exactly, but a little less) 18 Minutes....
But..What if the rate of Mules is nearly the same as horse (not exactly the same).. Lets say 12 mules have the rate of a little less than 1/32...
Now in the next 14 minutes...Horse will do 14/32 of the job...and mules will also do 13/32 of the job...Means 30/32 of the job....Do we have the job remaining? No!
They had to do 18/32 in less than 15 mins..they did 27/32 in less than 15 mins....
Hence Statement 1 is not sufficient..
(2) 48 mules can haul the same load of lumber in 16 minutes.
Means 48 Mules do 1/16th of the work in 1 minute
1 Mule does ...1/(16 x 48)th part of work in 1 minute
12 mules will do 12/(16 x 48) parts Means 1/64th part in 1 minute...
They are just half as fast as the horses
So for the next 14 minutes
Horses will do 14/32 Part of the work and Mules will do 14/64 Part of the work means 7/32 Part of the work...
Together they have done 21/32 Part of the work...we just needed 18/32 Part of the work in less than 15 minutes...Hence Statement 2 is sufficient ..answer B...
P.S..This was good for practice, but I don't think a question would come that would require so many calculations etc.
daviesj
