Monday, August 22, 2016

Time and Work 
Rule : If A can do a piece of work in D days, then A's 1 day's work = 1/D

Rule : If A's work efficiency is 2 times as compared to B then
 Ratio of work done by A and B is 2 :1
 Ratio of times taken by A and B to finish a work = 1 : 2 (inverse ratio)

Ex. A does a work in 10 days and B does the same work in 15 days. In how many days they together will do the same work ?
Time and Work
Time and work
So both will finish the work in 6 days
Ex. If A and B together can do a job in x days and A alone can do the same job in y days, then how many days it taken by B to complete the same job ?

Time and work
Time and work
Time and work
Rule : Let M1 person can do W1 work in D1 days with time T1 and M2 person can do W2 work in D2 days with time T2, then the relationship can be written as :

 Time and work
Ex. If 40 people can make 60 toys in 8 hrs, if 8 people leave the work, how many toys can make in 12 hrs ?

Solution : here M1= 40, D1= 8 hrs, W1= 60, M2= 32, D2 =12 hrs, W2= ?

Time and work

Time and work
Rule : If A, B and C can do a work in x, y and z days respectively then all of them working together can finish the work in :
    Time and work
Ex. A and B can do a piece of work in 12 days , B and C in 15 days and C and A can do in 20 days. How long would each take seperately to do the same work ?
Time and work

A+B+C can do the work in 5*2= 10 days

Time and work

Time and Work


Time and work
Ex. If 3 men or 4 women can do a work in 43 days, how long will 7 men and 5 women take to comlete the work ?
Solution:
3 men can complete 1 / 43 of work in a day
1 man can complete 1 /(43*3) work in a day
4 women can complete 1/ 43 of work in a day
1 woman can complete 1 / (43*4) of the work in a day
Time and work

So, 7 men and 5 women will complete the work in 12 days
Ex. Seven men can complete a work in 12 days. They started the work and after 5 days, two men left. In how many days will the work be completed by the remaning men ?
Soution :
7 men 1 day's work will be 1 / 12
1 man 1 day work will be 1 / (12*7) = 1 / 84
7 men 5 days work will be 5 / 12, so remaning work will be (1- 5/ 12) = 7 / 12
5 mens 1 day work will be 5 / 84

Time and work
Ex. A man, a women and a boy can complete a job in 3, 4 and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4 of a day ?
Solution :
1 man's + 1 woman's one day work = 1 / 3 + 1 / 4 = 7 / 12
work done by 1 man + 1 woman in 1 / 4 day = (7 / 12 )*( 1 / 4 )= 7 / 48
So the work remains=(1-7/48)= 41 / 48
Also work done by one boy in 1 / 4 day = (1 / 12 )*(1 / 4 ) = 1 / 48

Since 1 / 48 work is done by 1 boy in 1 / 4 days
So 41 / 48 work can be done by ( 41 / 48 ) * (48 / 1) = 41
Ex. 10 men and 15 women together can complete a work in 6 days. It takes 100 days for one man alone to complete the same work.How many days will be required for one woman alone to complete the same work ?
Solution :
1 man's one day work = 1 / 100
( 10 men's + 15 women's ) 1 day work= 1 / 6
15 women's one days work = (1 / 6 )- ( 10 / 100 ) = 1 / 15
1 woman 1 day work = ( 1 / 15* 15 ) = 1 / 225

So one woman will complete the work in 225 days
Ex. If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be :
Solution :
(6 men and 8 boys ) 1 day work = 1 / 10
Thie can be written as equeation form, let 1 man's one day work is M and one boy's one day work is B

6 M + 8 B = 1 / 10
Similarly 15 M + 20 B = 1 / 2 on solving M = 1 / 100, B = 1 / 200
Now ( 15 men + 20 boy ) 1 day's work = ( 15 / 100 )+ ( 20 / 100 ) = 1 / 4

So 15 men and 20 boys can do the work in 4 days.

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