A

[latex](\frac {1}{10} + \frac {1}{20}) \times (T-5) + \frac {5}{20} = 10[/latex] (T is the number of days in which the work is completed)

D

[latex]\frac {1}{7} + \frac {1}{5} = \frac {12}{35}[/latex] this much work is completed in 2 days.
So [latex]\frac {24}{35}[/latex] will be completed in 4 days
In the next day, [latex]\frac {29}{35}[/latex] work get completed in 5 days, so remaining work will be completed by Ram in 5[latex]\frac {6}{7}[/latex] days

A

Ratio of rates of working of A and B = 2 : 1.
So, ratio of times taken = 1 : 2.
B's 1 day's work = [latex]\frac{1}{12}[/latex]
i.e, A's 1 day's work = [latex]\frac{1}{6}[/latex] ; (2 times of B's work)
(A + B)'s 1 day's work = [latex][\frac{1}{6} + \frac{1}{12}] = \frac{3}{12} = \frac{1}{4}[/latex]
So, A and B together can finish the work in 4 days.

C

Let B take x days to complete the work, then A will take =[latex] \frac {x}{3} + \frac {x}{3} = \frac {2x}{3} + [/latex] days (as half work is completed in one third of the time)
[latex]\frac {3}{2x} + \frac {1}{x}\frac {1}{20} [/latex]
X = 50. So A will complete the work in [latex]\frac {100}{3}[/latex] days and B will complete the work in 50 days.
Ratio of work done by A and B – [latex]\frac {3}{100} :\frac {1}{50} = 3:2[/latex]
So A share = [latex] \frac {3}{5} \times 100 = 600[/latex]

A

Let B complete the work in X days so in one day work done by B is [latex]\frac {1}{x}[/latex]
As A do half work in one-sixth of the time so A will complete work in [latex]2 \times \frac {x}{6} = \frac {x}{3}[/latex] days
One day work of A and B i.e. [latex] \frac {3}{x} + \frac {1}{x} = \frac {1}{20}[/latex]. So we get x = 80
So time taken by A alone = [latex]\frac {80}{3}[/latex] days