2 Views

Question : A and B can do a piece of work in 10 days. B and C can do it in 12 days. C and A in 15 days. In how many days will C finish it alone?

Option 1: 24 days

Option 2: 30 days

Option 3: 40 days

Option 4: 60 days


Team Careers360 1st Jan, 2024
Answer (1)
Team Careers360 25th Jan, 2024

Correct Answer: 40 days


Solution : Given: A and B can do a piece of work in 10 days.
B and C can do it in 12 days.
C and A can do it in 15 days.
1 day work of A and B = $\frac{1}{10}$ -------(1)
1 day work of B and C = $\frac{1}{12}$ ------(2)
1 day work of A and C = $\frac{1}{15}$ ------(3)
Adding equations (1), (2), (3), we have:
2 × (A + B + C)'1 day work = $\frac{1}{10}+\frac{1}{12}+\frac{1}{15}$
⇒ 2 × (A + B + C)'s 1 day work = $\frac{6+5+4}{60}=\frac{1}{4}$
⇒ (A + B + C)'s 1 day work = $\frac{1}{8}$
1 day work of C = 1 day's work of (A + B + C) – 1 day's work of A and B = $\frac{1}{8}-\frac{1}{10}$
1 day work of C = $\frac{5–4}{40}=\frac{1}{40}$
So, C alone will finish the work in 40 days.
Hence, the correct answer is 40 days.

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