Time and Work-Basic test 1

Answer: Option C

Explanation

According to the above given formula, If M₁ persons can do W₁ work in D₁ days working T₁ hours a day and M₂ persons can do W₂ work in D₂ days working T₂ hours a day then, M₁T₁W₁= M₂T₁W₂

Here, M₁=6, T₁=16  M₂=8 T₂=?  and W₁=W₂=1

$$\begin{gathered} 6\times 16\times 1= 8\times {\mathrm{T}}_2\times 1 \\ {\mathrm{T}}_2=\frac{6\times 16\times 1}{8\times 1} =12 \mathrm{hours} \end{gathered}$$

Hence, 8 boys will complete the same work in 12 hours

Hence option C is correct

Answer: Option B

Explanation

Solution: According to the above given formula, P and Q can do a work in x days, Q and R can do the same work in y days, P and R can do it in z days. If they all work together P, Q, R can do that work in $\frac{\mathrm{xyz}}{\mathrm{xy}+\mathrm{yz}+\mathrm{zx}}$days.

So, 

$$\begin{gathered} \frac{4\times 8\times 12}{(4\times 8)+(8\times 12)+(12\times 4)}=\frac{384}{32+96+48} \\ =\frac{384}{176}=2.18 \mathrm{days} \end{gathered}$$

Hence, if all of them work together, the work will be completed in 2.18 days 

Hence option C is correct

Answer: Option A

Explanation

If P and Q together finish a piece os work in x days, and P alone can comple the same work in y days, then the time taken by B to complete the same work will be $\frac{\mathrm{xy}}{y-x}$days.

So, 

$\frac{18\times 12}{18-12}=\frac{216}{6}=36 days$

 Hence option A is correct

Answer: Option B

Explanation

According to the formula,

M₁D₁W₂=M₂D₂W₁

M₁=12, D₁=24, M₂=8, D₂=?

$D_2=\frac{12\times 24}{8}=12\times 3=36 days$

Hence option B is correct

Answer: Option A

Explanation

According to the given formula,

Given that

M₁= 20, D₁= 4, W₁ = 30,

M₂ = 20 - 4 = 16

D₂= 12, W₂ = ?

According to the formula, M₁D₁W₂=M₂D₂W₁

 $$\begin{gathered} 20\times 4\times W_2=16\times 12\times 30 \\ {W}_2=\frac{16\times 12\times 30}{20\times 4} \\ \Rightarrow 12\times 6=72 trees \end{gathered}$$

Hence option A is correct