Working alone at their respective constant rates, Ajay can complete

Question

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

KarishmaB · Accepted Answer

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)

CrackverbalGMAT · Answer

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

Assume total work = LCM ( 4,3 ) = 12 units

Ajay will do 12/4 = 3 units of work in 1 hr and Firoz will do 12/3 = 4 units of work in 1 hour.

Its given that Ajay worked for 2 hours and assume that frioz took 3 breaks for x hrs each. i.e Frioz work for only (2-3x) hrs

2 *3 + (2-3x)*4 = 12

6 + 8 - 12x = 12

2 = 12 x

x = 2/12 = 1/6 hr = 10 mins

Option B is the answer.

Thanks,
Clifin J Francis

MarmikUpadhyay · Answer

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 .

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Working alone at their respective constant rates, Ajay can complete

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