An air conditioner can cool the hall in 40 miutes while another takes 45 minutes to cool under similar conditions. If both air conditioners are switched on at same instance then how long will it take to cool the room approximately ?

Correct Answer: 12 days

Explanation:

3 4 × ( x - 2 ) x = ( x + 7 ) ( x - 10 )

? x 2 - 6 x - 280 = 0 

=> x= 20   and   x=-14

 so, the acceptable values is x=20 

Therefore, Total work =(x-2)x = 18 x 20 =360 unit

 Now   360 = 30 x k         

=> k=12 days

Correct Answer: 10

Explanation:

Let the number of workers be x.

Now, Using work equivalence method,

X + (X-1) + (X-2)+ . . . . + 1 = X *55% of X

 

=> [X * (X+1)] / 2 = X * (55X/100)    [because, Series is in AP. Sum of AP = {No. of terms (first term+ last term)/2} ]

Therefore, X = 10 

 

Correct Answer: 6

Explanation:

                       A   :   C    

 

Efficiency      5    :   3    

 

No of days   3x   :  5x     

 

Given that, 5x-6 =3x  => x = 3  

 

Number of days taken by A = 9  

 

Number of days taken by C = 15     

 

 

 

           B  :  C    

 

Days   2  :  3  

 

Therefore, Number of days taken by B = 10   

 

Work done by B and C in initial 2 days =  2 1 10 + 1 15= 1/3  

 

Thus,  Rest work =2/3  

 

Number of days required by A to finish 2/3 work = (2/3) x 9 = 6 days

Correct Answer: 25

Explanation:

(A+B+C) do 1 work in 10 days.

So (A+B+C)'s 1 day work=1/10 and as they work together for 4 days so workdone by them in 4 days=4/10=2/5

Remaining work=1-2/5=3/5

 

(B+C) take 10 more days to complete 3/5 work. So( B+C)'s 1 day work=3/50

Now A'S 1 day work=(A+B+C)'s 1 day work - (B+C)'s 1 day work=1/10-3/50=1/25

A does 1/25 work in in 1 day

Therefore 1 work in 25 days.

Correct Answer: 14 ( 2/7 )%

Explanation:

Let he initially employed x workers which works for D days and he estimated 100 days for the whole work and then he doubled the worker for (100-D) days.

D * x +(100- D) * 2x= 175x 

=>  D= 25 days 

Now , the work done in 25 days = 25x 

Total work = 175x

Therefore, workdone before increasing the no of workers =  25 x 175 x × 100 % =  14 2 7 %

Correct Answer: 7

Explanation:

Let 1 woman's 1 day work = x.

Then, 1 man's 1 day work = x/2 and 1 child's 1 day work  x/4.

So, (3x/2 + 4x + + 6x/4) = 1/7

28x/4 = 1/7 => x = 1/49

1 woman alone can complete the work in 49 days.

So, to complete the work in 7 days, number of women required = 49/7 = 7.

Correct Answer: 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                 

Correct Answer: 2:6:3

Explanation:

                                                A    :    B    :    C   

Ratio of efficiency               3     :    1    :    2   

Ratio of No.of days            1/3  :   1/1  :   1/2    

     or                                       2    :    6    :    3   

Hence A is correct.  

Correct Answer: 6 days

Explanation:

Work donee by A and B in the first two hours, working alternatively = First hour A + Second hour B = (1/4) + (1/12) = 1/3.

Thus, the total time required to complete the work  = 2 (3) = 6 days 

Correct Answer: 13 days

Explanation:

Ratio of times taken by A and B = 100 : 130 = 10 : 13.
Suppose B takes x days to do the work.

Then, 10 : 13 :: 23 : x     =>     x = ( 23 x 13/10 )     =>     x = 299 /10.

A's 1 day's work = 1/23 ;
B's 1 day's work = 10/299 .

(A + B)'s 1 day's work = ( 1/23 + 10/299 ) = 23/299 = 113 .

Therefore, A and B together can complete the work in 13 days.