### TIME AND WORK

1. Explanation :

A’s 1 hour's work = 1/8
B's 1 hour's work = 1/10
(A + B)'s 1 hour's work = (1/8) +(1/10)=9/40
Both A and B will finish the work in 40/9 days.

1. Explanation :

(A + B)'s 1 day's work = (1/4).
A's 1 day's work = (1/12).
B's 1 day's work =((1/4)-(1/12))=(1/6)
Hence, B alone can complete the work in 6 days.

1. Explanation :

A can complete the work in (7 x 9) = 63 hours.
B can complete the work in (6 x 7) = 42 hours.
A’s 1 hour's work = (1/63) and B's 1 hour's work =(1/42)
(A + B)'s 1 hour's work =(1/63)+(1/42)=(5/126)
Both will finish the work in (126/5) hrs.
Number of days. of (42/5) hrs each =(126 x 5)/(5 x 42)=3 days

1. Explanation :

(A + B)'s 1 day's work = (1/18)
(B + C)'s 1 day's work = (1/24)
and (A + C)'s 1 day's work = (1/36)
Adding, we get: 2 (A + B + C)'s 1 day's work =(1/18 + 1/24 + 1/36) =9/72 =1/8
(A +B + C)'s 1 day's work =1/16
Thus, A, Band C together can finish the work in 16 days.

1. Explanation :

(A’s 1 day’s work):(B’s 1 days work) = 2 : 1.
(A + B)'s 1 day's work = 1/18 Divide 1/18 in the ratio 2 : 1.
A’s 1 day's work =(1/18 * 2/3)= 1/27
Hence, A alone can finish the work in 27 days.

1. Explanation :

Ratio of times taken by A and B = 160 : 100 = 8 : 5.
Suppose B alone takes x days to do the job.
Then, 8 : 5 :: 12 : x = 8x = 5 x 12 =x = 7 1/2 days.

1. Explanation :

. Work done by A in 10 days =(1/80*10)=1/8 Remaining work = (1- 1/8) =7/ 8
Now,7/ 8 work is done by B in 42 days.
Whole work will be done by B in (42 x 8/7) = 48 days.
A’s 1 day's work = 1/80 and B's 1 day's work = 1/48
(A+B)'s 1 day's work = (1/80+1/48)=8/240=1/30 Hence, both will finish the work in 30 days.

1. Explanation :

C's 1 day's work = 1/3-(1/6+1/8)=24
A : B : C = Ratio of their 1 day's work = 1/6:1/8:1/24= 4 : 3 : 1.
A’s share = Rs. (600 *4/8) = Rs.300,
B's share = Rs. (600 *3/8) = Rs. 225.
C's share = Rs. [600 - (300 + 225») = Rs. 75.

1. Explanation :

(A + B)'s 2 days' work =(1/9+1/12)=7/36 Work done in 5 pairs of days =(5*7/36)=35/36
Remaining work =(1-35/36)=1/36
On 11th day, it is A’s turn. 1/9 work is done by him in 1 day.
1/36 work is done by him in(9*1/36)=1/4 day
Total time taken = (10 + 1/4) days = 10 1/4days.

1. Explanation :

(45 x 16) men can complete the work in 1 day.
1 man's 1 day's work = 1/720
45 men's 6 days' work =(1/16*6)=3/8 Remaining work =(1-3/8)=5/8
75 men's 1 day's work = 75/720=5/48
Now,5/48 work is done by them in 1 day.
5/8 work is done by them in (48 x 5/5)=6/8 days.

2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days.In how many days can 2 men and 1 boy do the work

1. Explanation :

Let 1 man’s 1 day’s work = x and 1 boy’s 1 day’s work = y.
Then, 2x+3y = 1/10 and 3x+2y = 1/8
Solving,we get: x = 7/200 and y = 1/100
(2 men + 1 boy)’s 1 day’s work = (2 x 7/200 + 1/100 x 1 ) = 16/200 = 2/25
So, 2 men and 1 boy together can finish the work in 25/2 =12 1/2 days