3 Views

Question : 3 men and 5 women together can complete a work in 6 days, whereas 4 men and 9 women together can do it in 4 days. How many women are required to do the same work in 7 days?

Option 1: 15

Option 2: 12

Option 3: 14

Option 4: 10


Team Careers360 16th Jan, 2024
Answer (1)
Team Careers360 21st Jan, 2024

Correct Answer: 12


Solution : Given: 3 men and 5 women together can complete a work in 6 days, whereas 4 men and 9 women together can do it in 4 days.
Let the efficiency of 1 man and 1 woman be $x$ and $y$.
According to the question,
$(3x + 5y)6 = (4x + 9y)4$
⇒ $18x + 30y = 16x + 36y$
⇒ $18x - 16x = 36 - 30y$
⇒ $2x = 6y$
⇒ $\frac{x}{y} = \frac{6}{2} = \frac{3}{1}$
⇒ $x : y = 3 : 1$
Let the total work $=(3 \times 3 + 5 \times 1)×6 = 84$
Let $n$ women complete the whole work in 7 days with the efficiency of 1,
⇒ $n \times 1 \times 7 = 84$
⇒ $n = \frac{84}{7} = 12$
Hence, the correct answer is 12.

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