A is twice as good as workman as B and together they finish a piece of work in 18 days. In how many days will B alone finish the work.

Answer: Option A

Explanation:

As Rahul and Sham together can finish work in 35 days.
1 days work of Rahul and Sham is 1/35
Rahul can alone complete this work in 60 days,
So, Rahul one day work is 1/60
Clearly, Sham one day work will be = (Rahul and Sham one day work) - (Rahul one day work)
\begin{aligned}
= \frac{1}{35} - \frac{1}{60} \\
= \frac{1}{84} \\
\end{aligned}

Hence Sham will complete the given work in 84 days.

Answer: Option B

Explanation:

As per question, A do twice the work as done by B.
So A:B = 2:1
Also (A+B) one day work = 1/18

To get days in which B will finish the work, lets calculate work done by B in 1 day =
\begin{aligned}
=\left(\frac{1}{18}*\frac{1}{3} \right) \\
= \frac{1}{54}
\end{aligned}
[Please note we multiplied by 1/3 as per B share and total of ratio is 1/3]

So B will finish the work in 54 days

Answer: Option C

Explanation:

Work done by A in 20 days = 80/100 = 8/10 = 4/5

Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 --- (1)

Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B)

Work done by A and B in 1 day = 1/15 ---(2)

Work done by B in 1 day = 1/15 – 1/25 = 2/75

=> B can complete the work in 75/2 days = 37 (1/2) days

Answer: Option B

Explanation:

Let 1 man's 1 day work = x
and 1 woman's 1 days work = y.
Then, 4x + 6y = 1/8
and 3x+7y = 1/10
solving, we get y = 1/400 [means work done by a woman in 1 day]

10 women 1 day work = 10/400 = 1/40

10 women will finish the work in 40 days

Answer: Option B

Explanation:

Firstly we will find 1 day work of both A and B, then by adding we can get collective days for them,
So,
A's 1 day work = 1/10
B's 1 day work = 1/15

(A+B)'s 1 day work =
\begin{aligned}
\left(\frac{1}{10}+\frac{1}{15} \right) \\
=\left(\frac{3+2}{30} \right) \\
= \frac{1}{6}
\end{aligned}

So together they can complete work in 6 days.