Horses and Mules

[srcc25anu]

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.

B

[Anju@Gurome]

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.

The question is asking whether all of them together can finish hauling the load in 15 minutes, i.e. whether it will take 15 minutes more to finish hauling the load after 12 mules have joined.

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

Statement 1: 12 mules works slower than 12 horses, so in 15 minutes they can do less than 180 horse minutes of work. Hence, 12 horses and 12 mules together in 15 minutes can do less than (180 + 180) = 360 horse minutes of work.

But they may or may not do more than 216 horse minutes of work.

Not sufficient

Statement 2: Now we can uniquely determine the work capacity of the mules in terms of horse minutes. Hence, we can definitely answer the question in YES or NO.

Sufficient

The correct answer is B.

[srcc25anu]

the way i approached it: i assumed Total workload = 240 units

16 Horses - in 24 mins - 240 workload
1 horse - in 1 min - 240 / (16 * 24) = 5/8 work
12 horses - in 14 mins - 5 * 14 * 12 / 8 = 105 units completed

Left work = 240 - 105 = 135 units

we add 12 mules. suppose mules speed of work = horse work speed
1 horse can do 1 work in 8/5 mins
24 horses - can finish 135 work in 8 * 135 / (5 * 24) = 9 mins

but if mule speed < horse speed total time to complete 135 units could exceed 15 mins or maybe not. we can't know for sure. That how i approached St 1 and went for A as not sufficient.