A can finish a work in 18 days and B can do same work in half the time taken by A. then working together, what part of same work they can finish in a day

Answer: Option D

Explanation:

A+B 1 day work = 1/8
B+C 1 day work = 1/12
A+B+C 1 day work = 1/6

We can get A work by (A+B+C)-(B+C)
And C by (A+B+C)-(A+B)

So A 1 day work =

$$\begin{aligned} \frac{1}{6}- \frac{1}{12} \\ = \frac{1}{12} \end{aligned}$$

Similarly C 1 day work =
$$\begin{aligned} \frac{1}{6}- \frac{1}{8} \\ = \frac{4-3}{24} \\ = \frac{1}{24} \end{aligned}$$

So A and C 1 day work =

$$\begin{aligned} \frac{1}{12} + \frac{1}{24} \\ = \frac{3}{24} \\ = \frac{1}{8} \end{aligned}$$

So A and C can together do this work in 8 days

Answer: Option B

Explanation:

1 woman's 1 day's work = 1/70
1 Child's 1 day's work = 1/140
5 Women and 10 children 1 day work =

$$\begin{aligned} \left(\frac{5}{70}+\frac{10}{140}\right) \\ = \frac{1}{7} \end{aligned}$$

So 5 women and 10 children will finish the work in 7 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:

Do not be confused, Take this question same as that of work done question's. Like work done by 1st puncture in 1 minute and by second in 1 minute.
Lets Solve it:

1 minute work done by both the punctures =

$$\begin{aligned} \left(\frac{1}{9}+\frac{1}{6} \right) \\ =\left(\frac{5}{18} \right) \\ \end{aligned}$$

So both punctures will make the type flat in
$$\begin{aligned} \left(\frac{18}{5} \right)mins \\ = 3\frac{3}{5} mins \end{aligned}$$

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