Time and Work-Basic test 2

Answer: Option D

Explanation

According to the question,

1 man= 2 woman= 3 boys

 ∴ 1 man + 1 woman + 1 boy

$=\left(3+\frac{3}{2}+1\right)boys =\frac{11}{2} boys$

Here,

M₁ = 3, D₁ =88

M₂ = $\frac{11}{2}$, D₂ = ?

So according to the formula,

     M₁ D₁ = M₂ D₂

∴  Required no. of days can becalculated as below,

$$\begin{gathered} 3\times 88=\frac{11}{2}\times D_2 \\ {D}_2=\frac{3\times 2\times 88}{11} \\ =3\times 2\times 8=48 days \end{gathered}$$

Hence option D is correct.

Answer: Option C

Explanation

According to the question,

In 1 day,

work completed by A= $\frac{1}{6}$

work completed by B= $\frac{1}{12}$

Work completed by= $\frac{1}{6}+\frac{1}{12}=\frac{2+1}{12}=\frac{3}{12}=\frac{1}{4}$

∴ (A+B) will complete the work in 4 days.

Hence option C is the correct 

Answer: Option C

Explanation

According to the question,

In 1 day

work completed by (A+B)= $\frac{1}{72}$

work completed by (B+C)= $\frac{1}{120}$

work completed by (A+C)= $\frac{1}{90}$

2(A+B+C)'s  1day's work $=\frac{1}{72}+\frac{1}{120}+\frac{1}{90}$

∴ (A+B+C)'s 1 day's work $=\frac{5+3+4}{360}\times \frac{1}{2}=\frac{12}{360\times 2}=\frac{1}{60}$

∴ No. of days in which A alone will complete the work= (A+B+C)'s 1day work - (B+C)'s 1 day work

$=\frac{1}{60}-\frac{1}{120}=\frac{2-1}{120}=\frac{1}{120}$

∴ A alone can finish the work in 120 days

Hence option C is the correct.

Answer: Option D

Explanation

According to the question,

Let us assume

time taken by B = x

then time taken by A = 2x

and time taken by C =3x

$=\frac{1}{x}+\frac{1}{2x}+\frac{1}{3x}=\frac{1}{12}$

⇒ $1+\frac{1}{2}+\frac{1}{3}=\frac{x}{12}$

$$\begin{gathered} \Rightarrow \frac{6+3+2}{6}=\frac{x}{12} \\ \Rightarrow 11=\frac{x}{2} \end{gathered}$$

∴   x=22

∴ Required no. of days= 2x= 2×22= 44 days

Hence option D is the correct .

Answer: Option C

Explanation

Here,

M₁ = 6, T₁ =16, W₂ =1

M₂ = 8, T₂ = ?, W₁ = 1

So according to the formula,

     M₁ D₁ W₂ = M₂ D₂ W₁

 $$\begin{gathered} \therefore 6\times 16\times 1=8\times T_2\times 1 \\ {T}_2=\frac{16\times 6}{8}=2\times 6=12 hrs \end{gathered}$$

 So, 8 boys complete the same work in 12 hours

 Hence option C is the correct.