Time and Work-Basic test 1

Answer: Option B

Explanation

According to the question,

A+B can complete a work in 3 days.

In 2 days,

(A+B) can complete⇒ $2\times \frac{1}{3}=\frac{2}{3}$ of the work

A alone in complete⇒ $1-\frac{2}{3}=\frac{1}{3}$of the work

B alone can complete⇒ $\frac{2}{3}-\frac{1}{3}=\frac{1}{3}$of the work

So in 1 day B can complete  ⇒$\frac{1}{6}$ of the work. Therefore, B alone will take 6 days to complete the work.

Hence option B is correct

Answer: Option B

Explanation

Here,

M₁ = 90, D₁ =25, W₂ =$1-\frac{2}{3}$

M₂ = 90-x, D₂ = 15, W₁ = $\frac{2}{3}$

So according to the formula,

     M₁ D₁ W₂ = M₂ D₂ W₁

_{$$\begin{gathered} \left(90\times 25\right) \left[1-\frac{2}{3}\right]=\left(90-x\right) \times 15\times \frac{2}{3} \\ 90\times 25\times \frac{1}{3}=10\left(90-x\right) \\ 75=90-X \\ x=90-75=15 men \end{gathered}$$}

Hence option B is correct

Answer: Option A

Explanation

Here,

M₁ = 36, D₁ =24, W₂ =$1-\frac{2}{5}$

M₂ = 36+x, D₂ = 24, W₁ = $\frac{2}{3}$

So according to the formula,

     M₁ D₁ W₂ = M₂ D₂ W₁

$$\begin{gathered} \left(36\times 24\right) \left(1-\frac{2}{5}\right)=\left(36+x\right)\times 24\times \frac{2}{5} \\ 36\times 24\times \frac{3}{5}=\left(36+x\right)\times 24\times \frac{2}{5} \\ 36\times 3=2\left(36+x\right) \\ 108=72+2x \\ x=\frac{36}{2}=18 men \end{gathered}$$

Hence option A is correct

Answer: Option A

Explanation

As per the question,

12 men = 18 women

So 1 man = $\frac{18}{12}$ women

⇒ 8 men = $\frac{18}{12}\times 8=12$ women

Here,

M₁ = 18, D₁ =14, W₂ =1

M₂ = 12+16, D₂ = ?, W₁ = 1

So according to the formula,

     M₁ D₁ W₂ = M₂ D₂ W₁

   $$\begin{gathered} 18\times 14\times 1=\left(12+16\right)\times D_2\times 1 \\ D_2=\frac{18\times 14}{28}=9 days \end{gathered}$$

Hence option A is correct

Answer: Option C

Explanation

Here,

M₁ = 20, D₁ =20, W₂ =$1-\frac{1}{3}$

M₂ = 20+x, D₂ = 25, W₁ = $\frac{1}{3}$

So according to the formula,

     M₁ D₁ W₂ = M₂ D₂ W₁

$$\begin{gathered} 20\times 20\times \left(1-\frac{1}{3}\right)=\left(20+x\right)\times 25\times \frac{1}{3} \\ 20\times 20\times \frac{2}{3}=\left(20+x\right)\times \frac{25}{3} \\ \Rightarrow 20+x=\frac{25}{3}\times \frac{3}{2}\times 20\times 20 \\ \Rightarrow 20+x=32 \\ x=32-20=12 men \end{gathered}$$

Hence option C is correct