Time and Work-Hard test 3

Answer: Option B

Explanation

Given in the question,

2 children= 1 man

∴ (16 children + 24 men)= (8+24) men = 32 men

We shall use the formula, M₁ D₁ W₂ = M₂ D₂ W₁

Here,

M₁ = 32, D₁ =18, W₁ =1,

M₂ = 24, D₂ = ?, W₂ = 1,

⇒ 32×18×1=24×D₂×1

D_{2$=\frac{32\times 18}{24}=8\times 3=24 days$}

Hence option B is the correct.

Answer: Option C

Explanation

According to the question,

In 1 day,

Ayesha can complete $\frac{1}{16}$^th of the work 

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

Ayesha and Amita together can complete 

$=\frac{1}{16}+\frac{1}{8}=\frac{1+2}{16}=\frac{3}{16}$ ^th of the work

∴ Ayesha and Amita together can complete the work  in $\frac{16}{3}$or $5\frac{1}{3} days$

Hence option C is the correct.

Answer: Option D

Explanation

According to the question,

Since, P can complete a work in 12 days working for 8 hours a day.

Work done in 1 day working for 1 hour a day

P can complete $=\frac{1}{8\times 12}=\frac{1}{96}$^th of the work

Q can complete $=\frac{1}{8\times 10}=\frac{1}{80}$^th of the work

(P+Q) together can complete$=\frac{1}{80}+\frac{1}{96}=\frac{11}{480}$^th of the work

Work done in 1 day working for 8 hours a day

(P+Q) together can complete$=\frac{11\times 8}{480}=\frac{11}{60}$^th of the work

∴  (P+Q) can complete the work in $=\frac{60}{11}=5\frac{5}{11}$ days

Hence option D is the correct.

Answer: Option A

Explanation

According to the question,

Number of pages copied by Subhash in 10 hours is 50

Number of pages copied in 1 hour by Subhash 

$=\frac{50}{10}=5$ pages

Subhash and Prakash together can copy $=\frac{300}{40}=\frac{15}{2}$ pages

Let time taken by prakash to copy 30 pages = x hours

∴ Number of pages copied by prakash in 1 hour $=\frac{30}{x}$

$$\begin{gathered} =\frac{30}{x}+5=\frac{15}{2} \\ =\frac{30}{x}=\frac{15}{2}-5=\frac{5}{2} \\ =\frac{30}{x}=\frac{5}{2} \\ x=\frac{2\times 30}{5}=12 hours \end{gathered}$$

Hence option A is the correct.

Answer: Option C

Explanation

According to the question,

In 1 day,

(A+B) together can complete $\frac{1}{5}$^th of the work 

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

So B alone can complete $=\frac{1}{5}-\frac{1}{8}=\frac{8-5}{40}=\frac{3}{40}$ of the work

∴B alone will complete the work in$=\frac{40}{3} or 13\frac{1}{3} days$

Hence option C is the correct.