Aptitude - Time and Work - Discussion

A = 15 = 1/15.
B = 10 =1/10.

1/10 * 2 =1/5.
1-1/5 = 4/5.
1/15 * 4/5 = 12 days.

A can do in 15 days.
B can do in 10 days.
Total work=lcm(30).
So, A 1 day work=30/15=2 units.
B 1 day work=30/10=3 units.
B worked for 2 days and left = 2*3=6.
The remaining work left is = 30-6=24.
Now, A alone can do 24 units =24/2=12 days.
Thus,the whole work is completed in 12 days.

Hope, it clears.

Why we add 2 for A's work? Explain please.

A can complete the work in 15 days.
B can complete the work in 10 days.
Assume Total work LCM(15,10) = 30 units
So, A's efficiency(1 day work) = 30/15 = 2 units
B's efficiency(1 day work) = 30/10 = 3 units

Now, Let the whole work was completed in x days.
Work completed by A and B together in 2 days = (Efficiency of A and B) * Days
= (2+3) * 2 = 10 units
Remaining work is completed by A (B had left) = Efficiency of A * (x - 2)
= 2 * (x - 2) Since, Number of days left = x - 2
10 units + 2*(x - 2) = Total work
10 + 2x - 4 = 30
=> x = 12 days.

A did in 15days.
B did in 10days .
One day work =(1/15 + 1/10) = 1/6.
Total work =1-1/6 = 5/6.
Remaining work: 5/6 * 1/10 = 12.

Take a look at easy method:-

A-15 days.
B-10 days.

Lcm of 10 and 15 =30.

A's 1 day work= 30/15=2.
B's 1 day work=30/10=3.

B left after 2 days, so,
B's 2 day work=3 2=6.

Now work left for A= 30-6=24.

Days required by A to complete the work= 24÷2= 12.
So, 12 days are the required answer.

a=15 days = 1/15 work for 1 day,
b=10 days =1/10 work for 1 day,
So in 2 days, 1/3 work is done.
1-1/3 = 2/3 work is remaining,
1/15 work 1 day,
2/3 work ? day,
10 days for A.

Total days are 10+2 = 12.

A -15 days.
B- 10.

A&B- 6.
The lcm of 15,10 ,6= 30,
A can do 2 in 1 day,
B can 3 in 1 day,
together 5 in 1 day,

Given the first two days, they worked together means 10w is done.
Remaining is 20w done by A in 10 day.
So 10 + 2(starting 2 day by A,b) = 12.

Thank you for the answer @Mr.Aj.

Let the work complete in x days as A's 1-day work is 1/15 (hence his x days work =x/15 and B's 2days work is =2/10.
x/15+2/10=1.
x/15 =1-2/10 .
x/15=4/5.
x=4/5 * 15=12days.