A piece of work can be done by 6 men and 5 women in 6 days or 3 men and 4 women in 10 days. It can be done by 9 men and 15 women in how many days ?

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 C

Explanation:

B's 5 days work =

$$\begin{aligned} \frac{1}{10}*5 = \frac{1}{2} \\ \text{Remaining work =} 1-\frac{1}{2} \\ = \frac{1}{2} \\ \text{A can finish work =}15*\frac{1}{2} \\ = 7.5 days \end{aligned}$$

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:

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 D

Explanation:

In this question we having, A's work, B's work and A+B+C work. We need to calculate C's work.
We can do it by,
(A+B+C)'s work - (A's work + B's work).

Let's solve it now:

C's 1 day work =

$$\begin{aligned} \frac{1}{4}- \left(\frac{1}{16} +\frac{1}{12} \right) \\ =\left(\frac{1}{4} - \frac{7}{48} \right) \\ = \frac{5}{48} \end{aligned}$$

So C can alone finish the job in 48/5 days,
Which is =
$$\begin{aligned} 9\frac{3}{5}days \end{aligned}$$