# CAT Quantitative Aptitude Questions | CAT Time and Work questions

###### CAT Questions | Time and work | Work Time
CAT Questions

The question is from Time and work. Efficiency of two people in relative terms is given and we need to find out the time required by one person. Classic Time and Work Question!!

Question 14: A can complete a task 4 hours lesser time than B takes to complete the same. If A and B together can complete the task in 288 minutes, how long does B alone take to complete the task?

1. 1 hr
2. 2 hrs
3. 3 hrs
4. 12 hrs

## Best CAT Coaching in Chennai

#### Batches filling fast. Starts Sat, May 25th, 2019

##### Method of solving this CAT Question from Pipes Cisterns and Work Time: Classic Work - Time Question!!

Let time taken by A be 'a' hours and time taken by B be 'a+4' hours
Then A does $$frac{1}{a}\\$ of the work in an hour. B does $\frac{1}{a+4}\\$ of the work in an hour. Together they take 288 minutes to finish the job , 288 minutes = $\frac{288}{60}\\$ = $\frac{24}{5}\\$ hours. Therefore, both A and B together complete $\frac{5}{24}\\$ every hour. $\frac{1}{a}\\$ + $\frac{1}{a+4}\\$ = $\frac{5}{24}\\$ $\frac{2a+4}{a$a+4$}$ = $\frac{5}{24}\\$ We get, 48a + 96 = 5$a2 + 4a
=> 5a2 - 28a - 96 = 0
=> 5a2 - 40a + 12a - 96 = 0
5a (a - 8) + 12(a - 8) = 0
(5a + 12)(a - 8) = 0 . Therefore, Since a cannot be negative, a = 8 hours.
Hence, a + 4 = 12 hours. Therefore, Time taken by B to complete the work on his own is 12 hours.

The question is "how long does B alone take to complete the task?"

##### Hence, the answer is "12 hrs".

Choice D is the correct answer.

###### CAT Coaching in Chennai

Next Weekend Batch Starts Sat, May 25th, 2019

###### Best CAT Coaching in ChennaiBatches filling fast

Personalised attention, Small batch sizes.

## CAT Online Coaching | CAT Arithmetic Videos On YouTube

#### Other useful sources for Arithmetic Questions | Pipes Cisterns; Time and Work Sample Questions

##### Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
10-C, Kalinga Colony, Bobbili Raja Salai
K.K.Nagar, Chennai. India. Pin - 600 078

##### How to reach 2IIM?

Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now
Email: prep@2iim.com