Time and Work-Basic test 2

Answer: Option C

Explanation

According to the question,

Time taken to complete the work by 

X= 10×4= 40 days

Y= $40\times \frac{100}{40}=100$days

Z= 13×3= 39 days

∴ Z will complete the work first.

Hence, option C is the correct.

Answer: Option A

Explanation

According to the question,

In 1 day,

(A+B) together can complete $\frac{1 }{8}$^th of the work

B can complete $\frac{1}{12}$^th of the work

∴ A can complete the work$=\frac{1}{8}-\frac{1}{12}=\frac{3-2}{24}=\frac{1}{24}$

So, A can complete the work in 24 days.

Now, B's 4 day's work$=\frac{4}{12}=\frac{1}{3}$

Remaining work$=1-\frac{1}{3}=\frac{2}{3}$

As, time taken by A to complete the work= 24 days

∴ Time taken by A to do $\frac{2}{3}$ of the work $=\frac{2}{3}\times 24=16$days

Hence option A is the correct.

Answer: Option A

Explanation

According to the question,

while B can do it in 6 days, B worked at it only for 4 days,

so, the work completed by B in 4 days$=\frac{1}{6}\times 4=\frac{2}{3}$

Remaining work$=1-\frac{2}{3}=\frac{1}{3}$

A can do this work in 10 days,

So, in 1 day A can complete$\frac{1}{10}$^th of the work

∴ $\frac{1}{3}$^rd of the work is finished by A in $\left(10\times \frac{1}{3}\right)=3\frac{1}{3}$ days

Hence option A is the correct.

Answer: Option E

Explanation

According to the question,

In 1 day,

P can complete $\frac{1 }{12}$^th of the work

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

 (P+Q) together can complete $=\frac{1}{12}+\frac{1}{8}=\frac{2+3}{24}=\frac{5}{24}$^th of the work

 ∴ (P+Q+R) will complete $\frac{1}{4}$^th of the work

   R can complete (P+Q+R)-(P+Q)

$$\begin{gathered} =\frac{1}{4}-\frac{5}{24} \\ =\frac{6-5}{24}=\frac{1}{24} \end{gathered}$$

 ∴ R will finish the work alone in 24 days.

 Hence option E is the correct.

Answer: Option A

Explanation

According to the question,

Let A,B and C take x, $\frac{x}{2}$ and $\frac{x}{3}$ days, respectively to complete the work.

So, in 1 day (A+B+C) will complete

$=\frac{1}{x}+\frac{2}{x}+\frac{3}{x}=\frac{6}{x}$^th of the work.

from question, $\frac{6}{x}=\frac{1}{2}$

[As (A+B+C)'s 1 day work =$\frac{1}{2}$]

⇒ x=12

∴ Time taken to complete the work by

A= 12 days

B= $\frac{12}{2}=6$ days

C= $\frac{12}{3}=4$ days

Hence option A is the correct .