LTI Time and Work Quiz 1

Ratio of times taken by A and B = 1 : 3.
The time difference is (3 - 1) 2 days while B takes 3 days and A takes 1 day.
If the difference of time is 2 days, B takes 3 days.
If difference of time is 60 days, B takes (3/2 x 60) = 90 days
So, A takes 30 days to do the work.
A's 1 day's work = 1/30
B's 1 day's work = 1/90
(A + B)'s 1 day's work = (1/30 + 1/90) = 4/90 = 2/45
A and B together can do the work in = 45/2 = 22 ½ days

Now (1-\frac{4}{5}) i.e \frac{1}{5} work is done by A and B in 3 days.
Whole work will be done by A and B in (3 x 5) = 15 days.
A's 1 day's work =1/25 , (A + B)'s 1 day's work = 1/15
B's 1 day's B's 1 day's work =(1/15 - 1/25) = 4/150 = 2/75

So, B alone would do the work in 75/2 = 37\frac{1}{2} 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.
P's1 hour's work =1/96, and Q's 1 hour's 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
Number of days of 8 hours each = (\frac{480}{11} \times \frac{1}{8})= \frac{60}{11} days =5\frac{5}{11} days

Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4.
Suppose Tanya takes x days to do the work
.5 : 4 :: 20 : x x =(4 x 20)/5
x = 16 days.
Hence, Tanya takes 16 days to complete the work.

Let 1 man's 1 day's work = x and 1 boy's 1 day's work = y.
Then, 6x + 8y= 1/10 , and 26x + 48y \frac{1}{2}
Solving these two equations, we get : x = 1/100 and y = 1/200
(15 men + 20 boy)'s 1 day's work = (15/100 + 20/200) = \frac{1}{4}
15 men and 20 boys can do the work in 4 days.

A's 2 day's work = (1/20 x 2) = 1/10
(A + B + C)'s 1 day's work = (1/20 + 1/30+ 1/60) = 6/60 = 1/10
Work done in 3 days =(1/10 + 1/10) = \frac{1}{5}
Now ⅕ work is done in 3 days.
Whole work will be done in (3 x 5) = 15 days.

Let us assume that Raghab can do the job in x days.
Then, Susmit can do the job in (x -50) days.
Therefore, time taken by Susmit = times of Raghab/3
Therefore, x-50 =x/3
=>3x – 150 = x
=>x = 75 days
Time taken by Raghab = 75 days
Time taken by Jack = 25 days
Therefore, Rose and Jack’s one day work =(75 + 25)/(75 x 25) = 4/75
Hence, they can complete the same work together in 75/4 days.

Work done by Atul in 4 days=(1/12) *4 = 1/3
Atul+Ankita+Sayak’s per day work=1/12 + 1/8 + 1/24 = 1/4
Work Done in 5 days= 1/3 + 1/4 = 7/12
If 7/12 is the work done in 5 days
Therefore the entire task will be done in (5*12)/7= 60/7 days.

Ankita’s 1 day’s work = 1/12
Ashish’s 1 day’s work = 1/18
Together in 1 day they can do = 1/12 + 1/18 = 5/36
In 3 days, they can do together = 3 x (5/36) = 5/12
So, the work left = 1 - 5/12 = 7/12

R’s 1 day work = 1/4 - (1/8 + 1/12) = 1/24
So, P’s wages : Q’s wages : R’s wages = 1/8 : 1/12 : 1/24 = 3 : 2 : 1
So, R is to be paid = (1/6) x 4800 = 800 Rs.