Aptitude Time and Work Online Test, Time and Work Mock Test

A’s 1 day’s work = 1/15 ;
B’s 1 day’s work = 1/20 ;
(A + B)’s 1 day’s work = (1/15 + 1/20) = 7/60
(A + B)’s 4 day’s work = (7/60 × 4) = 7/15
Therefore, Remaining work = (1-7/15) = 8/15

Ratio of times taken by A and B = 1 : 3.
The time difference is (3 – 1) 2 days while B take 3 days and A takes 1 day.
If difference of time is 2 days, B takes 3 days.
If difference of time is 60 days, B takes (3/2 × 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 = 22.5 days.

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 = 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) = 1/4
∴ 15 men and 20 boys can do the work in 4 days.

A’s 1 hour’s work = 1/4 ;
(B + C)’s 1 hour’s work = 1/3 ;
(A + C)’s 1 hour’s work = 1/2 .
(A + B + C)’s 1 hour’s work = (1/4 + 1/3) = 7/20
B’s 1 hour’s work = (7/12 – 1/2) = 1/12.
∴ B alone will take 12 hours to do the work.

(A + B)’s 1 day’s work = 1/10
C’s 1 day’s work = 1/50
(A + B + C)’s 1 day’s work = (1/10 + 1/50) = 6/50 = 3/25 ….(i)
A’s 1 day’s work = (B + C)’s 1 day’s work …. (ii)
From (i) and (ii), we get: 2 x (A’s 1 day’s work) = 3/25
A’s 1 day’s work = 3/50 .
⇒ B’s 1 day’s work = (1/10 – 3/50) = 2/50 = 1/25.
∴ So, B alone could do the work in 25 days.

Whole work is done by A in ( 20 x 5/4 ) = 25 days.
Now, (1 – 4/5) i.e., 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 .
Therefore B’s 1 day’s work = (1/15 – 1/25) = 4/150 = 2/75.
So, B alone would do the work in 75/2 = 37.5 days.

B’s 10 day’s work = (1/15 × 10) = 2/3
Remaining work = (1-2/3) = 1/3.
Now, 1/18 work is done by A in 1 day.
1/3 work is done by A in ( 18 x 1/3 ) = 6 days.

Let 1 man’s 1 day’s work = x and 1 woman’s 1 day’s work = y.
Then, 4x + 6y = 1/8 and 3x + 7y = 1/10 .
Solving the two equations, we get: x = 11/400 , y = 1/400
∴ 1 woman’s 1 day’s work = 1/400 .
⇒ 10 women’s 1 day’s work = (1/400 × 10) = 1/40.
Hence, 10 women will complete the work in 40 days.

(A + B)’s 20 day’s work = ( 1/30 x 20 ) = 2/3 .
Remaining work = ( 1 – 2/3 ) = 1/3 .
Now, 1/3 work is done by A in 20 days.
Therefore, the whole work will be done by A in (20 x 3) = 60 days.

1 woman’s 1 day’s work = 1/70
1 child’s 1 day’s work = 1/140
(5 women + 10 children)’s day’s work = (5/70 + 10/140) = (1/14 + 1/14) = 1/7
∴ 5 women and 10 children will complete the work in 7 days.

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 = (23×13 / 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 = 1/13.
Therefore, A and B together can complete the work in 13 days.

Number of pages typed by Ravi in 1 hour = 32/6 = 16/3 .
Number of pages typed by Kumar in 1 hour = 40/5 = 8.
Number of pages typed by both in 1 hour = (16/3 + 8) = 40/3.
Time taken by both to type 110 pages = (110 × 3/40) hours
= 8 1/4 hours (or) 8 hours 15 minutes.

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.

Suppose A, B and C take x, x/2 and x/3 days respectively to finish the work.
Then, (1/x + 2/x + 3/x) = 1/2
⇒ 6/x = 1/2
⇒ x = 12.
So, B takes (12/2) = 6 days to finish the work.

(A + B)’s 1 day’s work = (1/15 + 1/10) = 1/6
Work done by A and B in 2 days = (1/6 × 2) = 1/3.
Remaining work = (1 – 1/3) = 2/3
Now, 1/15 work is done by A in 1 day.
∴ 2/3 work will be done by a in (15 × 2/3) = 10 days.
Hence, the total time taken = (10 + 2) = 12 days.

Ratio of rates of working of A and B = 2 : 1.
So, ratio of times taken = 1 : 2.
B’s 1 day’s work = 1/12 .
∴ A’s 1 day’s work = 1/6 ; (2 times of B’s work)
(A + B)’s 1 day’s work = (1/6 + 1/12) = 3/12 = 1/4.
So, A and B together can finish the work in 4 days.

(20 x 16) women can complete the work in 1 day.
1 woman’s 1 day’s work = 1/320 .
(16 x 15) men can complete the work in 1 day.
1 man’s 1 day’s work = 1/240
So, required ratio = 1/240 : 1/320
= 1/3 : 1/4
= 4 : 3 (cross multiplied)

(A + B + C)’s 1 day’s work = 1/6 ;
(A + B)’s 1 day’s work = 1/8 ;
(B + C)’s 1 day’s work = 1/12 .

So, A and C together will do the work in 8 days.

(B + C)’s 1 day’s work = (1/9 + 1/12) = 7/36.
Work done by B and C in 3 days = (7/36 × 3) = 7/12.
Remaining work = (1-7/12) = 5/12.
Now, 1/24 work is done by A in 1 day.
So, 5/12 work is done by A in (24 × 5/12) = 10 days.

Let A’s 1 day’s work = x and B’s 1 day’s work = y.
Then, x + y = 1/30 and 16x + 44y = 1.
Solving these two equations, we get: x = 1/60 and y = 1/60
B’s 1 day’s work = 1/60 .
Hence, B alone shall finish the whole work in 60 days.