B

Say H alone can dig in H days
⇒ H can dig ([latex]\frac {1}{H}[/latex]) of well in one day.
P can dig [latex]\frac {1}{24}[/latex] of well in one day and J can dig [latex]\frac {1}{16}[/latex] of well in one day.
J, P and H all together can dig the well in 8 days
⇒ All together can dig [latex]\frac {1}{8}[/latex] of well in one day.
⇒ ([latex]\frac {1}{16}[/latex]) + ([latex]\frac {1}{24}[/latex]) + ([latex]\frac {1}{H}[/latex]) = [latex]\frac {1}{8}[/latex]
⇒ [latex]\frac {1}{H}[/latex] = ([latex]\frac {1}{8}[/latex]) – ([latex]\frac {5}{48}[/latex])
⇒ [latex]\frac {1}{H}[/latex] = [latex]\frac {1}{48}[/latex]
⇒ H = 48 days.

B

To understand it will break one hour in 12 segments of five minutes.
1st 5 Minutes = Thinks
2nd 5 minutes = Write.
3rd 5 minutes = Rest.
4th 5 Minutes = Write. [Because he can write up to 10 minutes if he thinks for 5 minutes.]
5th 5 minutes = Think. [He has completed 10 minutes of writing so he has to think.]
6th 5 minutes = Rest.
7th 5 minutes = Write.
8th 5 minutes = Write.
9th 5 minutes = Rest.
10th 5 minutes = Think.
11th 5 minutes = Write.
12th 5 minutes = Rest. [He has completed his 10 minutes of working. 5 minutes thinking + 5 Minutes writing.)
So, in one hour he will write 250 lines of codes.

B

To type a manuscript karthik took y hours.
Therefore his speed in typing = [latex]\frac{1}{y}[/latex]
He was called away after 2 hours of typing.
Therefore the work completed = [latex]\frac{1}{y} \times 2[/latex]
Therefore the remaining work to be completed = [latex]\frac{1-2}{y}[/latex]
(i.e.) work to be completed = [latex]\frac{(y-2)}{y}[/latex]

A

10 programmers can type 10 lines within 10 minutes
I.e., 1 programmer can type 1 line within 10 minutes
Also 1 programmer can type 6 lines within 60 minutes
Hence, to get 60 lines typed in 60 minutes,
We need [latex]\frac{60}{6}[/latex] = 10 programmers

D

Number of men and number of days taken to complete work are inversely proportional.
Number of men × Number of days is constant.
∴ Number of days by 25 men to complete the work = [latex]\frac{(20 × 15)}{25}[/latex] = 12 days.