71 Views

Question : A and B alone can do a piece of work in 4 and 9 days, respectively. In how many days will the work be completed, if they both work on alternate days, starting with B?

Option 1: $5\frac{1}{3}$

Option 2: $5\frac{2}{3}$

Option 3: $5$

Option 4: $5\frac{1}{4}$


Team Careers360 14th Jan, 2024
Answer (1)
Team Careers360 19th Jan, 2024

Correct Answer: $5\frac{2}{3}$


Solution : Given: Time taken by A to complete the work = 4 days
Time taken by B to complete the work = 9 days
They both work on alternate days, starting with B.
Let the total work = LCM of 4 and 9 = 36 units
A’s 1 day's work = $\frac{36}{4}$ = 9 units
B’s 1 day's work = $\frac{36}{9}$ = 4 units
If they work on alternate days they will finish (4 + 9) = 13 units of work in 2 days,
In 4 days they will finish (13 × 2) = 26 units of work,
On the 5th day, B will finish 4 more units,
So, (26 + 4) = 30 units of work is done.
We have remaining (36 – 30) = 6 units of work, but A can finish 9 units in a day.
So, he will able to finish 6 units in $\frac{6}{9}=\frac{2}{3}$ day itself.
$\therefore$ Total work will be completed in $(5+\frac{2}{3})=5\frac{2}{3}$ days
Hence, the correct answer is $5\frac{2}{3}$.

SSC CGL Complete Guide

Candidates can download this ebook to know all about SSC CGL.

Download EBook

Know More About

Related Questions

TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books