Rate of working of Preeti, \(r_p = \frac{100}{75} = \frac{4}{3}\)

Rate of working of Mariska, \(r_m = \frac{50}{30} = \frac{5}{3}\)

Quantity A -

They make 180 sandwiches together, \(180 = r_{combined}*time taken\)

\(180 = (r_p + r_m)*t\)

\(180 = (\frac{4}{3} + \frac{5}{3})*t\)

\(t = 180*\frac{3}{9} = \)60 mins

Quantity B -

Mariska works for 30 mins alone, in that time she makes, \(r_m*30 = \frac{5}{3}*30 = \)50 sandwiches.

Now 110 - 50 = 60 sandwiches are left to be made.

\(60 = (r_p + r_m)*t\)

\(60 = (\frac{4}{3} + \frac{5}{3})*t\)

\(t = 60*\frac{3}{9} = \)20 mins

Therefore, total time = 30 + 20 = 50 mins

Hence, Answer is A

Preeti's rate is \(\frac{100}{75} =\frac{4}{3}\), while Mariska's rate is \(\frac{50}{30} =\frac{5}{3}\). This means that when they work together their rate becomes \(\frac{4}{3}+ \frac{5}{3} = \frac{9}{3}\).

Quantity A is computed taking into account that P and M together make 3 sandwich a minute, thus they make 180 sandwich in 60 minutes.

Quantity B: Mariska alone prepares 5 sandwich in 3 minutes, thus working 30 minutes she makes 50 sandwiches. When they work together they have 60 sandwiches left to do at a rate of 3 sandwiches a minute, thus it takes other 20 minutes to finish the sandwiches. 30 + 20 = 50 minutes.

Answer A

Let's determine each person's rate in terms of sandwiches per MINUTE

Rate = output/time

GIVEN: Preeti can make 100 sandwiches in 1 hour and 15 minutes.
In other words, Preeti can make 100 sandwiches in 75 minutes.
Rate = 100/75 = 4/3 sandwiches per MINUTE

GIVEN: Mariska can make 50 sandwiches in 30 minutes
Rate = 50/30 = 5/3 sandwiches per MINUTE


QUANTITY A: The time it would take Preeti and Mariska to make a total of 180 sandwiches
Their COMBINED rate = 4/3 + 5/3 = 9/3 = 3 sandwiches per MINUTE
time = output/rate
So, time = 180/3 = 60 minutes



QUANTITY B: The time it would take to make 110 sandwiches if Mariska worked alone for 30 minutes and then Mariska and Preeti worked together to finish the job
Output = (rate)(time)
So, in 30 minutes and at a rate of 5/3 sandwiches per MINUTE), the output = (5/3)(30) = 50
So, Mariska can make 50 sandwiches in 30 minutes.
110 - 50 = 60
So, we must now determine the time for Mariska and Preeti to make the remaining 60 sandwiches.

time = output/rate
So, time = 60/3 = 20 minutes

So, the total time to make 110 sandwiches = 30 minutes + 20 minutes = 50 minutes

Quantity A is greater

Answer: A

Cheers,
Brent
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