10 Views

Question : A, B, and C can do a job in 6 days, 12 days and 15 days respectively. After $\frac{1}{8}$th of the work is completed, C leaves the job. The rest of the work is done by A and B together. The time taken to finish the work is:

Option 1: $5\frac{5}{6}$ days

Option 2: $5\frac{1}{4}$ days

Option 3: $3\frac{1}{2}$ days

Option 4: $3\frac{3}{4}$ days


Team Careers360 20th Jan, 2024
Answer (1)
Team Careers360 24th Jan, 2024

Correct Answer: $3\frac{1}{2}$ days


Solution : Given: A, B, and C can do a job in 6 days, 12 days, and 15 days respectively.
Total work = Efficiency × Time
Total work is the LCM of (6, 12, 15) = 60 units
Efficiency of A $=\frac{60}{6}=10$
Efficiency of B $=\frac{60}{12}=5$
Efficiency of C $=\frac{60}{15}=4$
C has done $\frac{1}{8}$th of the work, which is $\frac{1×60}{8} = \frac{15}{2}$ units
Work left is given as $60-\frac{15}{2} = \frac{105}{2}$ units
Left work is done by both A and B together.
$\therefore$ Time taken by A and B $=\frac{\text{Work}}{\text{Efficiency}} = \frac{105}{2×(10+5)}=\frac{105}{30} = 3\frac{1}{2}$ days
Hence, the correct answer is $3\frac{1}{2}$ days.

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