A can do a job in 16 days, B can do same job in 12 days. With the help of C they did the job in 4 days. C alone can do the same job in how many 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.

Answer: Option C

Explanation:

(A+B)'s 1 day work = 1/4

A's 1 day work = 1/12

B's 1 day work =

$$\begin{aligned} \left( \frac{1}{4} - \frac{1}{12} \right) \\ = \frac{3-1}{12} \\ = \frac{1}{6} \\ \end{aligned}$$

So B alone can complete the work in 6 days

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 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:

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