'A' can do a work in 10 days. How much work does he do in 1 day.
If we go by traditional method the prompt answer would be 1/10 of the work.
But multiplicity of such fraction based calculations in a particular question is not going to make our life simpler but harder.
So if we take the whole work to be done as 100% and if we keep some of the percentage values of fractions in our mind, our life becomes easier. So, for the above question in 1 day 10%(100%/10) of the work is done.
This could be applied to the questions related to pipes and cisterns.
To make our concept more clear let us deal with some of the questions.
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{some %age values of fractions}
1/1=100% ½=50% 1/3=33.33% ¼=25%
1/5=20% 1/6=16.66% 1/7=14.28% 1/8=12.5%
1/9=11.11% 1/10=10% 1/11=9.09% 1/12=8.33%
1/13=7.69% 1/14=7.14% 1/15=6.66% 1/16=6.25%
1/17=5.88% 1/18=5.55% 1/19=5.26% 1/20=5%
Q.1: Anup can do a piece of work in 10 days and Jagdeesh can do the same work in 15 days.
1. In how many days the work will be completed if both works together.
2. In how many days the work will be completed if Megha who can complete the same work in 30 days joins.
3. In how many days the work will be completed if Alankar who destructs the work done in 25 days joins joins the two.
4. In how many days the work will be completed if Anup and Jagdeesh do the work on alternate days. Anup starting first.
5. With reference to the q.4 who will conclude the work.
6. With reference to q.4 when will the work be completed if Alankar who destructs the work in 25 days does the work every third day.
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solutions: 1. Anup can do in 1 day={100%/10}=10% of the work.
Jagdeesh can do in 1 day= {100%/15}=6.66 % of the work.
if both of them works together, the work done by them in 1
day=10%+6.66%=16.66%
so no. of days the total work(100%) will be done=100/16.66=6.002 or 6 days.
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2. Megha can do in 1 day={100/30}=3.33% of the work.
Anup and Jagdeesh can do the work in 1 day=16.66%. and when Megha joins them in one day the percentage of work done=(16.66+3.33)%=19.99% or 20%
No. of days the work will be completed=100/20=5 days.
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3. Anup and Jagdeesh can do the work in 1 day=16.66%.
Alankar can destroy the % age of work in 1 day=100/25=4 %.
Total work done in 1 day=16.66-4=12.66 %
So total work will be done in=100/12.66=7.88 or 8 days.
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4. Since Anup starts first, on the 1st day %age of work done=10%
On the 2nd day ,only Jagdeesh work,so work done=6.66%
3rd day=10%
4th day=6.66%......so on.
every two day 16.66 % of the work is done.
so in 6 pairs of days 99.96% of the work is done.or say 12 days. But still some work is left to be done,so in 13 days the work will be completed.
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5. If we go by explanation given in solution.4 on 12th day Jagdeesh will do the work. So on the 13th day which is the last day, Anup will do the work, so Anup will conclude the work.
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6.On the 1st day only Anup will do the work. Work done on 1st day=10%
On the 2nd day only Jagdeesh will do the work, work done after expiry of 2nd day=10%+6.66%=16.66%
On the third day Alankar will destroy the work= - 4%( negative sign as work is not being done but being destroyed )
At the end of third day total work completed=16.66%(work done upto 2nd day) less 4%( work destroyed in the third day=16.66-4=12.66%
So every third day 12.66% of the total work will be completed.
So in 7 group of every three days 88.62%{12.66*7} of the work is done.In other way, we can say that after expiry of 21 days(7*3) 88.62 % of the work is done.
On 22nd day work completed =(88.62+10)=98.62%.
So we see on the 23rd day only 1. 38%(100 - 98.62) of the work is to be done. And on the third day Jagdeesh will do the work ,who can do 6.66% of work in one day. So the work will be completed on the 23 rd day and Jagdeesh will do the conclusion.
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