Time and Work-Hard test 3

Answer: Option C

Explanation

Let A can complete the work in x days and B in 3x days.

=3x-x=60

=2x=60

⇒ x=30 days

A can finish the work in 30 days and B can finish the same work in 90 days.

∴ in 1 day (A+B) can complete.$\frac{1}{30}+\frac{1}{90}=\frac{4}{90}$^th of the work

∴(A+B) can finish the complete work in$=\frac{90}{4}$ $or 22\frac{1}{2} days$

Hence option C is the correct.

Answer: Option A

Explanation

According to the question,

Time taken by B $=\frac{100}{100\pm x}$ x total days taken by A

$$\begin{gathered} =\frac{100}{160}\times 12 \\ =\frac{15}{2} or 7\frac{1}{2} days \end{gathered}$$

 Hence option A is the correct.

Answer: Option C

Explanation

Time taken to complete the work by

C=x days

A=3x days

According to the question,

$$\begin{gathered} =\frac{1}{3x}+\frac{1}{{\displaystyle \frac{3x}{2}}}+\frac{1}{x}=1 \\ =\frac{1}{3x}+\frac{2}{3x}+\frac{1}{x}=1 \\ =\frac{1+2+3}{3x}=1 \\ \Rightarrow \frac{6}{3x}=1 \end{gathered}$$

$$\begin{gathered} \Rightarrow \frac{2}{x}=1 \\ \therefore x=2 \end{gathered}$$

Time taken to by Ais 3x

So, 3×2=6 days

Hence option C is the correct.

Answer: Option A

Explanation

We shall use the formula, $\frac{kl}{k^2-1}$

[Here, k= number of times, l=given days]

Given, k=3, l=40

 $$\begin{gathered} =\frac{3\times 40}{3^2-1} \\ =\frac{3\times 40}{8}=15 days \end{gathered}$$

 Hence option A is the correct.

Answer: Option E

Explanation

According to the question,

16 men and 12 women together can complete a work in 8 days and 20 men can complete the same work in 16 days

So, (16 men+12 women)×8 days=20 men×16 days

⇒ 16 men+12 women=40 men

⇒ 12 women=(40-16)=24 men

∴ 1 woman = 2 men    ...(1)

⇒ 16 women =32 men ...(2)

Now, 20 men can complete the work 16 day's

So, 32 men can complete the same work in $\left(\frac{16\times 20}{32}\right)days=10 days$

as 1 woman = 2 men

16 women can complete the same work in 10 days

Hence option E is the correct.