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21 Jun 2021, 04:15
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
63% (02:12) correct
37%
(02:36)
wrong
based on 275
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Working alone at their respective constant rates, Ajay can complete a certain job in 4 hours, while Firoz can do the same job in 3 hours. Ajay and Firoz worked together on the job and completed it in 2 hours, but while Ajay worked this entire time, Firoz worked for some of the time and took 3 breaks of equal length. How many minutes long were each of Firoz’ breaks?
(A) 5 minutes
(B) 10 minutes
(C) 15 minutes
(D) 20 minutes
(E) 25 minutes
(A) 5 minutes
(B) 10 minutes
(C) 15 minutes
(D) 20 minutes
(E) 25 minutes
23 Jun 2021, 23:19
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Bunuel
Rate of work of Ajay = 1/4th work per hr
Rate of work of Firoz = 1/3rd work per hr
Ajay worked for 2 hrs so completed 2*(1/4) = 1/2 the work in that time.
So Firoz did rest of the work in Time = Work/Rate = (1/2)/(1/3) = 3/2 hrs i.e. in 1 hr 30 mins.
So Firoz rested for total 30 mins i.e. his each of the 3 breaks were of 10 mins.
Answer (B)
General Discussion
23 Jun 2021, 21:10
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Bunuel
Let work done = w, rate of Ajay = a, rate of Firoz = f, time taken by Ajay = 4 hours, time taken by Firoz = 3 hours, time taken by both = 2 hours.
Hours worked by Ajay when working together= 2 hours, Hours worked by Firoz when working together = t.
From data:
a * 4 = w
=> a = \(\frac{w}{4}\)
Similarly f = \(\frac{w}{3}\)
Also,
a * 2 + f * t = w
=> \(\frac{w}{4}\) * 2 + \(\frac{w}{3}\) * t = w
=> t = \(\frac{3}{2}\) = 1.5 hours
=> Firoz took a break of 30 minutes in total.
=> Firoz took 3 breaks of 10 minutes each.
So, correct answer is option B.
