7 Views

Question : X and Y together can do a work in 10 days. Y and Z together can do the same work in 15 days. Z and X together can do the same work in 12 days. In how many days can Z alone do the same work?

Option 1: 80 days

Option 2: 60 days

Option 3: 40 days

Option 4: 50 days


Team Careers360 23rd Jan, 2024
Answer (1)
Team Careers360 24th Jan, 2024

Correct Answer: 40 days


Solution : Given,
X and Y together can do a work in 10 days.
Y and Z together can do the same work in 15 days.
Z and X together can do the same work in 12 days.
Let the total work = LCM (10, 15, 12) = 60
⇒ Efficiency of X + Y = $\frac{60}{10}$ = 6 units/day
⇒ Efficiency of Y + Z = $\frac{60}{15}$ = 5 units/day
⇒ Efficiency of Z + X = $\frac{60}{12}$ = 4 units/day
⇒ Efficiency of 2(X + Y + Z) = 15 units/day
$\therefore$ Efficiency of (X + Y + Z) = 7.5 units/day
Now, Efficiency of Z = 7.5 – 6 = 1.5 units/day
$\therefore$ Z alone can do the work = $\frac{60}{1.5}$ = 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