10 Views

Question : A can do a certain task in 1.5 times the number of days in which B and C together can do it. If A and B together can do the task in 30 days, and C alone can do it in 120 days, how many days will B take to do this task alone?

Option 1: 75

Option 2: 45

Option 3: 60

Option 4: 50


Team Careers360 16th Jan, 2024
Answer (1)
Team Careers360 17th Jan, 2024

Correct Answer: 60


Solution : Work done by (A + B) in 1 day $=\frac{1}{30}$
Work done by C in 1 day $=\frac{1}{120}$
Work done by (A + B + C) in 1 day $=\frac{1}{30} + \frac{1}{120} = \frac{4 + 1}{120} = \frac{5}{120} = \frac{1}{24}$
The ratio of the time taken by A to the time taken by B and C together = 1.5 : 1 = 3 : 2
Let A complete the task in 3$k$ days and B and C together, in 2$k$ days.
Work done by (A + B + C) in 1 day $=\frac{1}{2k}+\frac{1}{3k} =\frac{1}{24}$
$⇒\frac{5}{6k} =\frac{1}{24}$
$\therefore k=20$
Work done by A in 1 day = $\frac{1}{60}$
Work done by B in 1 day = Work done by (A + B) in 1 day – Work done by A in 1 day $=\frac{1}{30} - \frac{1}{60}=\frac{1}{60}$
$\therefore$ B completed the task in 60 days.
Hence, the correct answer is 60 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