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Q #31
⏰ :

Directions: Read the following information to answer the question.

A, B and C are to make 100 toys. In a day, they can together make 25 toys. A starts to work alone and makes 32 toys in some days. A then leaves and B and C works to make the remaining toys. It takes 8 days overall to make the 100 toys. How many days will it take for A to make 256 toys alone?

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Discuss
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A, B and C together could make 100 toys in 100/25 = 4 days
i.e. A + B + C => 4 days
Total time taken when first A worked then B + C worked -> 8 days (i.e. 2 x 4)
Hence, it is as if A and (B+C) worked alternatively for 4 days each to complete the 100 days
So, A can make 32 toys in 4 days => In a day, A can make = 32/4 = 8 toys/day
To make 256 toys, A will take = 256/8= 32 days


Q #32
⏰ :

Directions: Read the following information to answer the question.

A certain number of pages need to be typed. A, B and C are assigned to do this job. However, C leaves after 4 days when 40% of the job was complete. In this way, it takes 13 days to finish the job. Also, B can type twice as fast as A. How much would the fastest worker take to type the entire set of pages alone?

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Discuss
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A and B take 9 days to complete the remaining 60% of the job.
Therefore, in one day A and B can complete – 60/9 = 20/3 of the job
Since B is twice as fast as A,
B can finish = 20/3* 2/3 = 40/9 of the job in a day
A can finish = 20/3 * 1/3 = 20/9 of the job in a day
In the first 4 days. A and B would have finished = 20/3 * 4 = 80/3 of the job
Therefore, C would have finished = 40 % - 80/3  = 40/3 of the job in 4 days
So, in a day C finishes = 40/12  of the job
Thus, clearly B is the fastest among the three workers

 


Q #33
⏰ :

Directions: Read the following information to answer the question.

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 (in hrs)?

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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


Q #34
⏰ :

Directions: Read the following information to answer the question.

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?

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Given, 295 m was mined out of which first 5 days – planned.
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


Q #35
⏰ :

Directions: Read the following information to answer the question.

Number of units of a good that can be produced by a factory is directly proportional to the square of the number of workers, square root of the number of machines and to the number of hours put in. The factory produces 200 goods when 4 people work for 8 hours each with 4 machines. When 3 people work for 12 hours each with 9 machines, how many goods will be produced?

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G α No of workers2
G α √(No. of Machines)
G α No of hours
200 α 42 * √4 * 8
200 α 16 * 2 * 8
200 α 256
200 = k x 256
K = 200/256 
K = 25/32