Aptitude - Time and Work - Discussion

X"s one day work is 1/20.
so he worked 4 days alone which is,
4* 1/20 = 1/5 remember the Confusion avoider formula below,
(Days * single day"s work( together or alone, this case alone by X) = completed work) remember this
when we know days RHS is Completed work, if Days not known RHS is Pending work
1/5 work is completed out entire work 1
entire work - completed work = 1-1/5 = 4/5 or 80% which is pending work
pending work is 4/5 which is done by X and Y
one day's work of X and Y is 1/20 + 1/12 = 2/15 this is 1 day"s work and Inverse is the Days. If you ask WHY see X 1/20 is one day's work of X, inverse which is 20 is the number of days. Is it clear?

15/2 * 4/5= 6 days
Use this formula.

Days * single day's work ( this case by X and Y) = remaining or completed work.
Days we have to find * 2/15 = 4/5 which gives 4/5* 15/2 =6.

Now 6 days for 80% or 4/5 of the job by x and Y and 4 days for initial 1/5 or 20% of the job by x.

So, total 10 days.

x can do a work in 20 days
y can do a work in 12 days
To find total work ,take LCM of 20 and 12 i.e 60
Therefore Total work =60
x's 1 day capacity =60/20 =3
Y's 1 day capacity =60/12 =5

Since x alone did work for 4 days,
4*3=12 ,
12 work done in 4 days
there fore remaining work = 60-12 =48
Remaining work was completed by both
remaining work / (x's per day capacity +y's per day capacity)=48/6= 6
therefore remaining work was completed in 6 days
Total work was completed in 4 + 6 = 10 days.

I hope this is useful...

The work done by A in 4 days = 4* work done by A in one day.

The work done by A in one day= 1/20.
The work done by a in 4 days= 4/20.

So, the left over work is 1-(4/20) = 16/20.

After 4 days A and B work together.
Work is done by A and B together in one day=(1/20)+(1/12) = 8/60.
No of days needed by A and B to complete the job=(left overwork)/(Work done by A and B together in one day).

= (16/20)/(8/60).
= 6 days.

So total days taken is time taken by A alone + time taken by A and B together.
=6+4.
=10 days.

Chocolate method:

LCM of 20 and 12 is 60. there are 60 chocolates and.

A requires 20 days to eat 60 chocolates. He eats 3 chocolates per day.
B requires 12 days to eat 60 chocolates. He eats 5 chocolates per day.

For the first 4 days A alone eats the chocolates. total number of chocolates eaten up by A in 4 days is 12.
Remaining chocolates are (60-12) = 48.

A and B together eats 8 chocolates per day.
So to eat 48 chocolates they will need 48/8 = 6 days.

Total number of days = 4+6 = 10.

One days work of X=1/20.
One days work of Y=1/12.
Four days work is. 4[1/X = 1/20],
=> 4/X = 4/20,
=>4/X. = 1/5
1 is the whole work.
1-1/5 = 4/5.
Then 4/5 work is to be done.

X's and Y's one day work is = 1/20+1/12=2/15.

Let "K" be the number of days taken by X and Y to complete the work.

1 day --->2/15.
K days --->4/5.
4/5 ×1 = K× 2/15.
4/5 ×15/2 = K.
K = 2×3 = 6 days.
4 days work of X.
6 days work of X and Y.

4 + 6 =10 days.

One shortcut method.

Total work assumes as 1unit.
Use option to Slove this
1.we know that x's 1day work= 1/20.
Same y's=1/12
Choose option no. a, i.e .6 if x work for 6 days so y work for 2 days because y start working after 4 days so.
6/20+2/12 = 1,
Is not equal to 1.
So, the answer is not 6.
Take another i.e.10.
If x takes 10 days, y takes 6 days.
10/20+6/12 = 1.
Lhs=rhs . So the ans. Is 10days.

X 1 days work = 1/20.

Y 1 days work = 1/12.

X work for 4 days ---> 4/20 = 1/5.

Remaining work to be done--->1-1/5 = 4/5.

After 4 days Y is join with X to work.

So X+Y 1 day's work = (1/20+1/12) = 2/15 ---> X+Y finish work in 15/2 days.

So X+Y finish 4/5 part of work in 15/2*4/5 ----> 6 days.

Total days ---> 4+6 = 10 days.

In 1 day 1/20 th work.

Let us assume a takes x days to complte it

As B joins 4 days later he has only x-4 days remaining.

They both work respectively with their capacities and finish the one complete work

Hence

(1/20th work) * x days + (1/12th work) * (x-4) days = 1 full work

=> x/20 + (x-4)/12 = 1

=> x = 10days

X=>20 and Y=>12.

L.C.M. of 20&12=>60.
The efficiency of X is 3 and of Y is 5,

3 * 4 = 12 (here 3 is the efficiency of X and 4 is the no: of days he worked alone)
remaining work=60-12=48,
8*x=48 (here 3+5=8),
x=48/8; x=6.

According to the question we want to know how many days work went on
so, 4+6 =10 days.

1day per x work as = 1/20 && y= 1/12..

x do work 4days ..then 4*1/20=1/5 then remaining work= 1-1/5=4/5

Remaining work's done by y i.e. 1work ---> 12
4/5 ------> x
x=4/5 * 12 = 48/5 = 9.6day nearly = 10days..

It's good method to understand GUYS..!