A can do a certain job in 25 days which B alone can do in 20 days. A started the work and was joined by B after 10 days. The number of days taken in completing the wotk were ?

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 B

Explanation:

Please note in this question, we need to answer part of work for a day rather than complete work. It was worth mentioning here because many do mistake at this point in hurry to solve the question

So lets solve now,
A's 1 day work = 1/18
B's 1 day work = 1/9 [because B take half time than A]

(A+B)'s one day work =

$$\begin{aligned} \left(\frac{1}{18}+\frac{1}{9} \right) \\ =\left(\frac{1+2}{18} \right) \\ = \frac{1}{6} \end{aligned}$$

So in one day 1/6 work will be done.

Answer: Option A

Explanation:

Ratio of times taken by A and B = 1:3
Means B will take 3 times which A will do in 1 time

If difference of time is 2 days, B takes 3 days
If difference of time is 10 days, B takes (3/2) * 10 =15 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 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