Time and Work Quiz – 1

One day's work of A, B and C = (1/24 + 1/30 + 1/40) = 1/10.

C leaves 4 days before completion of the work, which means only A and B work during the last 4 days.

Work done by A and B together in the last 4 days = 4 (1/24 + 1/30) = 3/10.

Remaining Work = 7/10, which was done by A,B and C in the initial number of days. 

Number of days required for this initial work = 7 days. 

Thus, the total numbers of days required = 4 + 7 = 11 days.

P can complete the work in (12 x 8) hrs = 96 hrs 

Q can complete the work in (8 x 10) hrs=80 hrs 

Therefore, P's 1 hour work=1/96   and Q's 1 hour work= 1/80

(P+Q)'s 1 hour's work =(1/96) + (1/80) = 11/480. So both P and Q will finish the work in 480/11 hrs  

Therefore, Number of days of 8 hours each = (480/11) x (1/8) = 60/11

Let the two conditioners be A and B

 'A' cools at 40min

 'B' at 45min

 Together = (a x b)/(a + b)

= (45 x 40)/(45 + 40)

= 45 x 40/85

= 21.1764   = 22 min

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

Let A's 1 day's work=x and B's 1 day's work=y

Then x+y = 1/40 and 20x+60y=1 

Solving these two equations , we get : x= 1/80 and y= 1/80

Therefore B's  1 day work = 1/80

Hence,B alone shall finish the whole work in 80 days

Work done 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 

 

1 man's 1 day work = 1/108

12 men's 6 day's work = 1/9 x 6 = 2/3

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

16 men's 1 day work = 1/108 x 16 = 4/27

4/27 work is done by them in 1 day.

1/3 work is done by them in 27/4 x 1/3 = 9/4 days.

9M + 12B ----- 12 days ...........(1)

12M + 12B ------- 10 days........(2)

10M + 10B -------?

108M + 144B = 120M +120B

24B = 12M => 1M = 2B............(3)

From (1) & (3)

18B + 12B = 30B ---- 12 days

20B + 10B = 30B -----? => 12 days.

4/10 + 9/x = 1     => x = 15 

 Then both can do in 

1/10 + 1/15 = 1/6     => 6 days

From the given data,

=> (2 M + 3W) 8 = (3M + 2W)7

=> 16M + 24W = 21M + 14 W

=> 10W = 5M

=> 2W = M

=> 14W × ? = 7W × 8

? = 4 days