4 men and 6 women finish a job in 8 days, while 3 men and 7 women finish it in 10 days. In how many days will 10 women working together finish it ?

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:

A's 1 day work = 1/16
B's 1 day work = 1/12

As they are working on alternate day's
So their 2 days work = (1/16)+(1/12)
= 7/48

[here is a small technique, Total work done will be 1, right, then multiply numerator till denominator, as 7*6 = 42, 7*7 = 49, as 7*7 is more than 48, so we will consider 7*6, means 6 pairs ]

Work done in 6 pairs = 6*(7/48) = 7/8

Remaining work = 1-7/8 = 1/8

On 13th day it will A turn,
then remaining work = (1/8)-(1/16) = 1/16

On 14th day it is B turn,

1/12 work done by B in 1 day

1/16 work will be done in (12*1/16) = 3/4 day

So total days =

$$\begin{aligned} 13\frac{3}{4} \end{aligned}$$

It may be a bit typical question, but if are not getting it in first try then give it a second try. Even not, then comment for explanation for this. We will be happy to help you.

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 C

Explanation:

Work done by A in l0 days = (1/25) *10 = 2/5
Remaining work = 1 - (2/5) = 3/5
(A+B)s 1 days work = (1/25) + (1/20) = 9/100

9/100 work is done by them in 1 day.
hence 3/5 work will be done by them in (3/5)*(100/9)
= 20/3days.

Total time taken = (10 + 20/3) = 16*(2/3) days

Answer: Option B

Explanation:

C's 1 day's work =

$$\begin{aligned} \frac{1}{3}- \left(\frac{1}{6} +\frac{1}{8} \right) \\ =\left(\frac{1}{3} - \frac{7}{24} \right) \\ = \frac{1}{24} \\ A:B:C = \frac{1}{6}:\frac{1}{8}:\frac{1}{24} \\ = 4:3:1 \\ C's Share = \frac{1}{8}* 3200 \\ = 400 \end{aligned}$$
If you are confused how we multiplied 1/8, then please study ratio and proportion chapter, for small information, it is the C ratio divided by total ratio.