Time and Work-Hard test 3

Answer: Option E

Explanation

According to the question,

In 1 day

Manoj can complete $\frac{1}{12}$^th of the work 

Salim can complete $\frac{1}{8}$^th of the work

∴ Raj can complete$=2\times \frac{1}{8}=\frac{1}{4}$ ^th of the work

Then, (Manoj+Salim+Raj) can complete 

$$\begin{gathered} =\frac{1}{12}+\frac{1}{8}+\frac{1}{4} \\ =\frac{2+3+6}{24}=\frac{11}{24} \end{gathered}$$

∴  (Manoj+Salim+Raj)'s together will complete the work in $\frac{24}{11}$ or $2\frac{2}{11}$ days.

 Hence option E is the correct.

Answer: Option A

Explanation

According to the question,

In 1 day,

(1 man+ 1 women +1 child)'s can complete $\frac{1}{3}$^th of the work

∴ 1 Woman can complete $=\frac{1}{3}-\frac{1}{6}-\frac{1}{18}\Rightarrow \frac{6-3-1}{18}=\frac{1}{9}$^th of the work

So, the woman alone can complete the work in 9 days.

Hence option A is the correct.

Answer: Option B

Explanation

According to the question,

In 1 day,

(B+C) together can complete $\frac{1}{8}$^th of the work     ...(1)

(A+B) together can complete $\frac{1}{12}$^th of the work   ...(2)

(A+C) together can complete $\frac{1}{16}$^th of the work   ...(3)

On adding equations 1, 2 and 3, we get 2(A+B+C)'s 1 day work

$$\begin{gathered} =\frac{1}{8}+\frac{1}{12}+\frac{1}{16} \\ =\frac{6+4+3}{48}=\frac{13}{48} \end{gathered}$$

⇒ (A+B+C)'s 1 days work$=\frac{13}{48\times 2}=\frac{13}{96}$

∴ A, B and C together can complete the work in $\frac{96}{13}$$or 7\frac{5}{13} days$

Hence option B is the correct.

Answer: Option C

Explanation

According to the question,

In 1 day,

A can complete $\frac{1}{12}$^th of the work 

B can complete $\frac{1}{24}$^th of the work

C can complete $=\frac{1}{36}$^th of the work

Then, (A+B+C) together can complete 

$$\begin{gathered} =\frac{1}{12}+\frac{1}{24}+\frac{1}{36} \\ =\frac{6+3+2}{72}=\frac{11}{72} \end{gathered}$$

∴ (A+B+C) together will complete the work in $\frac{72}{11} or 6\frac{6}{11} days$

Hence option C is the correct.

Answer: Option A

Explanation

Let A and C complete work in x days.

In 1 day,

(A+B) together can complete $\frac{1}{8}$^th of the work   ...(1)

(B+C) together can complete $\frac{1}{12}$^th of the work ...(2)

(C+A) together can complete $\frac{1}{x}$^th of the work   ...(3)

Then, (A+B)+(B+C)+(C+A) together can complete $\frac{1}{8}+\frac{1}{12}+\frac{1}{x}$^th of the work

∴ 2(A+B+C)$=\frac{5x+24}{24\times 2x}$

Given in the question (A+B+C) together can complete $\frac{1}{6}$^th of the work 

$\Rightarrow \frac{1}{6}=\frac{5x+24}{48x}\Rightarrow 30x+144=48x$

$\therefore x=\frac{144}{18}=8 days$

Hence option A is the correct.