in Quantitative Aptitude edited by
351 views
2 votes
2 votes

When they work alone, $\text{B}$ needs $25\%$ more time to finish a job than $\text{A}$ does. They two finish the job in $13$ days in the following manner: $\text{A}$ works alone till half the job is done, then $\text{A}$ and $\text{B}$ work together for four days, and finally $\text{B}$ works alone to complete the remaining $5\%$ of the job. In how many days can $\text{B}$ alone finish the entire job?

  1. $20$
  2. $16$
  3. $22$
  4. $18$
in Quantitative Aptitude edited by
13.4k points
351 views

1 Answer

1 vote
1 vote

Given that, when they work alone,  $\text{B}$ needs $25 \%$ more time to finish a job than $\text{A}$.

Let $100x$ days taken by $A$ to finish the job.

 Then,  time taken by $\text{B}$  to finish the job $=  100x \times \frac{125}{100} = 125x$ days.

$\text{A}$ works alone till half the job is done.

$\Rightarrow \frac{100x}{2} = 50x$ days

Then, $ \text{A}$ and $\text{B}$ work together for $4$ days.

And finally $ \text {B}$ works alone to complete the remaining $5\%$ of the job.

$\Rightarrow 125x \times \frac {5}{100}= \frac {25x}{4}$ days

 $\text A$ and $\text B$ finish the job in $13$ days in the following manner :

$ \Rightarrow 50x +4+ \frac {25x}{4}=13$

$ \Rightarrow 50x + \frac {25x}{4}=13-4$

$ \Rightarrow \frac {200x+25x}{4}=9$

$ \Rightarrow 225x=36$

$ \Rightarrow x= \frac {36}{225}$

$\therefore$ Number of days in which $\text{B}$ alone can finish the job $=125x = 125 \times \frac {36}{225}=20$ days.


$\textbf{Short Method:}$ 

$\begin{array}{ccc} &  \textbf{A} & \textbf{B} \\ \text{Time:} & 100 & 125 \\ & 4 & 5 \\\hline \text{Efficiency:} & 4 & 5 \end{array}$

  • A work alone $ = 50\%$
  • B work alone $ = 5\%$
  • A and B together work $ = 100\% – 50\%-5\% = 45\%$

 Let $x$ days they take to finish the entire job.

  • $4$ days $\longrightarrow 45\%$
  • $x$ days $\longrightarrow 100\%$

$x = \frac{4 \times 100\%}{45\%} = \frac{80}{9}$ days

Total work $ = \frac{80}{9} \times9 = 80$ units.

Therefore, B alone can finish the job $ = \frac{80}{4} = 20$ days.

Correct Answer $: \text {A}$

edited by
10.3k points
Answer:

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true