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**Question 11: Pipe A can fill a tank in 12 hours. When it works along with Pipe B, it can fill the tank in 8 hours. In how many hours can pipe B fill the same tank independently?**

(A) 8 hrs

(B) 12 hrs

(C) 24 hrs

(D) 16 hrs**Answer: CExplanation:**

Let the capacity of the tank be C.

Rate of Pipe A = C/A

Rate of Pipe B = C/B

Rate of Pipe A and Pipe B together = C/A + C/B = C/8

C/12 + C/B = C/8

C/B = C/8 - C/12 = C/24

Pipe B independently will take 24 hours to fill the tank.

The question is

Hence, the answer is "24 hrs"

(A) K = 253.125

(B) K = 100/163

(C) K = 25/256

(D) K = 16/29

G α No of workers

G α √(No. of Machines)

G α No of hours

200 α 4

200 α 16 * 2 * 8

200 α 256

200 = k x 256

K = 200/256

K = 25/32

When 3 people work for 12 hours each with 9 machines, the number of goods that will be produced is equal to 25/32 * 3

The question is **"When 3 people work for 12 hours each with 9 machines, how many goods will be produced?"**

Hence, the answer is "K = 253.125".**Question 13: A can complete a task in 12 days. B can complete the task in 18 days. If A and B work on this same task in alternate days starting with A, in how many days do they finish the entire task?**

(A) 10.8 days

(B) 14.33 days

(C) 11 days

(D) 8.4 days**Answer: B****Explanation:**

A can complete a task in 12 days and B can complete the task in 18 days. So,

In one day, A can do 1/12, in one day B can do 1/18.

In two days, they can complete 1/12 + 1/18 = which is 5/36.

In 4 days, they can finish 10/36, and so on.

We can have 7 such sets of 2days each.

So, at the end of 14 days, they would have done 35/36 of task.

On the 15th day A would begin work with 1/36of the task to finish. He can finish 1/12 in a day. So, he would take one-third of a day. So, they can finish the whole task in 14.33 days.

The question is **"how many days do they finish the entire task?"**

Hence, the answer is "14.33 days".**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?**

(A) 1 hr

(B) 2 hrs

(C) 3 hrs

(D) 12 hrs**Answer: D****Explanation:**

Let time taken by A be 'a' hours and time taken by B be 'a+4' hours

Then A does 1/a of the work in an hour.

B does 1/a+4 of the work in an hour.

Together they take 288 minutes to finish the job , 288 minutes = 288/60 = 24/5 hours.

Therefore, both A and B together complete 5/24 every hour.

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?"**

Hence, the answer is "12 hrs".**Question 15: A Two pipes can fill a tank in 12 hrs and 18 hrs respectively. The pipes are opened together but due to a pipe leakage , it takes 48 minutes extra to fill the tank, If the tank is full, what time will it take to completely empty due to the leakage.**

(A) 72 hrs

(B) 84 hrs

(C) 96 hrs

(D) 112 hrs**Answer: A****Explanation:**

Time taken to fill the tank completely without leakage = 1/(1/12)+(1/18) hrs

= 1/(9+6)/108 = 108/15 = 7 hours and 12 minutes

Given, it takes 48 minutes extra with the leakage. So, total time taken = 8 hours

= 8 (Where, x is the time taken by the leakage to completely empty the tank)

The question is **"what time will it take to completely empty due to the leakage."**

Hence, the answer is "72 hrs".}**Question 16: A cistern of capacity 40 litres has an inlet and an outlet pipe. When both the pipes are opened at once, it takes 8 minutes to fill the cistern. However, if the outflow rate is increased 1.5 times, the cistern never gets filled. Which of the following can be the outflow rate?**

(A) 8 litres/minute

(B) 6 litres/minute

(C) 12 litres/minute

(D) 9 litres/minute**Answer: C****Explanation:**

Initially, net flow in the tank = 40 litres/ 8 minutes = 5 litres/minute

Now, the increase in outflow should be greater than 5 litres/min for the tank to fill up.

Increase in outflow = 1.5x – x = 0.5x

Only in option C, 0.5 * 12 = 6 litres/min > 5 litres/min

The question is "Which of the following can be the outflow rate?"

Hence, the answer is "12 litres/minute".**Question 17: A cistern of 475 litres is completely filled using pipes A and B, with Pipe A being open for 5 more hours than pipe B. If we are to interchange the operating hours of the two pipes than pipe A would have pumped half the water as much as pipe B, then find the time for which pipe B was open. Also, given that if the two pipes were open simultaneously the tank would fill in 19 hours.**

(A) 10 hrs

(B) 14 hrs

(C) 16 hrs

(D) 20 hrs**Answer: C****Explanation:**

The 475 litres is filled in 19 hours by the two pipes when they are opened simultaneously.

Therefore, rate of water flow by A and B,

A + B = 475/19 = 25 litres/hour………….(1)

Let pipe B was opened for t hours

Then, pipe A was opened for t + 5 hours

A x (t+5) + B x t = 475

(A + B) x t + 5A = 475

25t + 5A = 475

=> 5t + A = 95

Now, using option analysis

a) t = 10 => 5 x 10 + A = 95 => A = 45 (not possible from (1))

b) t = 14 => 5 x 14 + A = 95 => A = 25 (not possible from (1) as B can’t be zero)

c) t = 16 => 5 x 16 + A = 95 => A = 15

The question is** "if the two pipes were open simultaneously the tank would fill in 19 hours."**

Hence, the answer is "16 hrs".**Question 18: A mining team made a plan to mine up to 300 m in a certain number of days. After working as per plan for 5 days, they added new members to the team and hence could mine 5 m more per day. In this way, 4 days before the planned date, they had mined 295 m. How many meters of mining was initially planned for each day?**

(A) 30 m

(B) 12.5 m

(C) 15 m

(D) 7.5 m**Answer: C****Explanation:**

Given, 295 m was mined out of which first 5 days – planned. Using option analysis:

a) 30 * 5 + (30 + 5) * (300/30 – 5 – 4) = 150 + 35 * 1 = 185 ≠ 295

b) 12.5 * 5 + 17.5 * (300/12.5 – 5 – 4) = 62.5 + 17.5 * 15 = 325 ≠ 295

c) 15 * 5 + 20 * (300/15 – 5 – 4)1 = 75 + 20 * 11 = 295

The question is** "How many meters of mining was initially planned for each day?"**

Hence, the answer is "15 m".**Question 19: Ajay and Suraj can water a garden in 45 minutes and 40 minutes respectively. They started working together but after some time Ajay left to watch a cricket match. Suraj hurriedly finished the work in next 23 minutes and joined Ajay. After how many minutes had Ajay left?**

(A) 9 min

(B) 8 min

(C) 7 min

(D) 10 min**Answer: A****Explanation:**

Suraj took 23 minutes to finish the remaining work = 23/40

Work finished by Ajay and Suraj together = 17/40

Time taken = = 9 mins

The question is **"how many minutes had Ajay left?"**

Hence, the answer is "9 min".**Question 20: Bibhor takes 3 hours to fetch as much water as Ahmed can fetch in 2 hours. Deepak takes 5 hours to fetch as much water as Bibhor can fetch in 4 hours. A tank takes 20 hours to fill if all work together. What time would Bibhor take to fill the tank alone?**

(A) 50 hrs

(B) 56 hrs

(C) 77 hrs

(D) 66 hrs**Answer: D****Explanation:**

Let the work done by Ahmed be 60 (LCM of 2,3,4,5)

So, work done per hour by:

Ahmed – 60/2 = 30

Bibhor – 60/3 = 20

Bibhor in 4 hours – 20 x 4 = 80

Deepak – 80/5 = 16

Therefore, total work done in an hour = 30 + 20 + 16 = 66

If all 3 work for 20 hours, total work done = 66 * 20

If Bibhor alone has to work, time taken to do 66 * 20 of work = 66 * 20/20 (work done by Bibhor in 1 hour)

= 66 hours

The question is **"What time would Bibhor take to fill the tank alone?"**

Hence, the answer is "66 hrs".

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