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Q:

A contractor  undertook a project to complete it in 20 days which needed 5 workers to work continuously for all the days estimated. But before the start of the work the client wanted to complete it earlier than the scheduled time, so the contractor calculated that  he needed to increase 5 additional  men every 2 days to complete the work in the time the client wanted it:

If the work was further increased by 50% but the contractor continues to increase the 5 workers o every 2 days then how many more days are required over the initial time specified by the  client.

A) 1 day B) 2 days
C) 5 days D) None of these
 
Answer & Explanation Answer: B) 2 days

Explanation:

Total work = 100+50 = 150man-days

In 8 days 100 man-days work  has been completed. Now on 9th and 10th day there will be 25 workers. So in 2 days they wll complete additional 50 man- days work. Thus the work requires 2 more days.

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Filed Under: Time and Work

Q:

In a public bathroom there are n taps 1,2,3...n. Tap1 and Tap2 take equal time to fill the tank while Tap3 takes half the time taken by Tap2 and Tap4 takes half the time taken by Tap3. Similarly each next number of tap takes half the time taken by previous number of Tap i.e, K-th Tap takes half the time taken by (K-1)th Tap. If the 10th tap takes 2 hours to fill the tank alone then what is the ratio of  efficiency of 8th tap and 12th tap, respectively?

A) 4:1 B) 5:3
C) 16:1 D) 1:16
 
Answer & Explanation Answer: D) 1:16

Explanation:

Time taken by 8th tap = 2 x 2 x 2= 8 hours

Time taken by 12th tap = 2x (1/2) x (1/2)  = 1/2 hour

Ratio of time taken by 8th tap and 12th tap = 8 : 1/2 =16:1

Therefore, Ratio of efficiencies of 8th tap and 12th tap =1:16

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Filed Under: Time and Work

Q:

A tank has an inlet and outlet pipe. The inlet pipe fills the tank completely in 2 hours when the outlet pipe is plugged. The outlet pipe empties the tank completely in 6 hours when the inlet pipe is pluggeed.

If there is a lekage also which is capable of draining out the liquid from the tank at half of the  rate of outet pipe,them what is the time taken to fill the emty tank when both the pipes are opened?

A) 3 hours B) 4 hours
C) 5 hours D) None of these
 
Answer & Explanation Answer: B) 4 hours

Explanation:

Rate of leakage = 8.33% per hour

Net efficiency = 50 - (16.66 + 8.33)= 25%

Time required = 100/25 = 4 hours

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Filed Under: Time and Work

Q:

A single reservoir supplies the petrol to the whole city, while the reservoir is fed by a single pipeline filling the reservoir with the stream of uniform volume. When the reservoir is full and if 40,000 liters of petrol is used daily, the suply fails in 90 days.If 32,000 liters of petrol is used daily, it fails in 60 days. How much petrol can be used daily with out the supply ever failing? 

A) 64000 liters B) 56000 liters
C) 78000 liters D) 60000 liters
 
Answer & Explanation Answer: B) 56000 liters

Explanation:

Let x liter be the per day filling and v litr be the capacity of the reservoir, then 

      90x + v = 40000 * 90     -----(1)

      60x + v= 32000 * 60     ------(2)

solving eq.(1) and (2) , we get

      x = 56000

Hence , 56000 liters per day can be used without the failure of supply.

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Filed Under: Time and Work

Q:

A is twice efficient as B and together they do the same work in as much time as C and D together. If C and D can complete the work in 20 and 30 daysrespectively, working alone ,then in how many days A can complete the work individually:

A) 12 days B) 18 days
C) 24 days D) 30 days
 
Answer & Explanation Answer: B) 18 days

Explanation:

                                              A     +      B        =      C     +     D 

                                              |              |                 |             | 

    Ratio of efficiency         10x   +    5x               9x     +   6x 

                                             |________|                 |_________|   

                                                   15x                           15x 

Therefore , ratio of efficiency of A:C  =10:9 

Therefore,  ratio of days taken by A:C = 9:10 

Therefore, number of days taken by A = 18 days                 

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Filed Under: Time and Work

Q:

Application of Inverse Proportion

If 20 persons can do a piece of work in 7 days then calculate the number of persons require to complete the work in 28 days

Answer

Number of persons * days = work  


20 * 7 = 140 man- days 


 


Now,  x * 28  = 140 men- days


=> x =5         


Therefore in second case the required number of person is 5.


 


Second method:


Since work is constant, therefore  M1 x D1= M2 x D2


20 x 7 = M2 x 28


=> M2 = 5 


 

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Subject: Time and Work

Q:

The diluted wine contains only 8 liters of wine and the rest is water. A new mixture whose concentration is 30%, is to be  formed by replacing wine. How many liters of mixture shall be replaced with pure wine if there was initially 32 liters of water in the mixture ?

A) 4 B) 5
C) 8 D) None of these
 
Answer & Explanation Answer: B) 5

Explanation:

           Wine                         Water

            8L                              32L

            1                :               4

           20 %                           80% (original ratio)

           30 %                           70% (required ratio)

 

In  ths case, the percentage of water being reduced when the mixture is being replaced with wine.

 

so the ratio of left quantity to the initial quantity is 7:8

 

Therefore , 78=1-K40

 

=> K = 5 Lit

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Filed Under: Alligation or Mixture
Exam Prep: CAT , Bank Exams
Job Role: Bank PO , Bank Clerk

Q:

From the 50 liters of milk, 5 liters of milk is taken out and after it 5 liters of water is added to the rest amount of milk. Again 5 liters of milk and water is drawn out and it was replaced by 5 liters of water. If this process is continued  similarly for the third time, the amount of milk left after the third replacement: 

A) 45L B) 36.45L
C) 40.5L D) 42.5L
 
Answer & Explanation Answer: B) 36.45L

Explanation:

General Formula:

Final or reduced concentration = initial concentration x 1-amount being replaced in each operationtotal amountn

where n is the number of times the same operation is being repeated. The "amount being replaced" could be pure or mixture as per the case. similarly ,"total amount" could also be either pure or mixture. Here amount being replaced denotes the quantity which is to be withdrawn in each time.

 

Therefore,    50×1-5503

= 36.45 L

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Filed Under: Alligation or Mixture