10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?

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 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:

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

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.