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 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 A

Explanation:

To calculate the answer we need to get 1 man per day work and 1 woman per day work.

Let 1 man 1 day work =x
and 1 woman 1 days work = y.
=> 6x+5y = 1/6
and 3x+4y = 1/10
On solving, we get x = 1/54 and y = 1/90

(9 men + 15 women)'s 1 days work =
(9/54) + (15/90) = 1/3

9 men and 15 women will finish the work in 3 days

Answer: Option C

Explanation:

Suppose B takes x dáys to do the work.
As per question A will take
$$\begin{aligned} 2* \frac{3}{4} * x = \frac{3x}{2}days \end{aligned}$$

(A+B)s 1 days work= 1/18
1/x + 2/3x = 1/18 or x = 30 days

Answer: Option A

Explanation:

In this type of question, where we have one person work and together work done. Then we can easily get the other person work just by subtracting them. As,

Son's one day work =
$$\begin{aligned} \left(\frac{1}{3}-\frac{1}{5} \right) \\ =\left(\frac{5-3}{15} \right) \\ = \frac{2}{15} \end{aligned}$$

So son will do whole work in 15/2 days
which is =

$$\begin{aligned} 7\frac{1}{2}days \end{aligned}$$

Answer: Option C

Explanation:

Let 1 man 1 day work = x
1 boy 1 day work = y

then 5x + 2y = 4(x+y)
=> x = 2y
=> x/y = 2/1
=> x:y = 2:1