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 hr
- 2 hrs
- 3 hrs
- 12 hrs

12 hrs

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(a^{2} + 4a

=> 5a^{2} - 28a - 96 = 0

=> 5a^{2} - 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?"**

Choice D is the correct answer.

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