# 2 men and 5 boys can finish a piece of work in 4 days, while 3 men and 6 boys can finish it in 3 days. Find the time taken by one man alone to finish the work and that taken by one boy alone to finish the work.

1st Method

Let the time taken by one man alone to finish the work and that taken by one boy alone to finish the work be u and v days respectively.

Time taken by 1 man to finish one part of the work = 1/u days

Time taken by 1 boy to finish one part of the same work = 1/v days

According to question -

2 men and 5 boys can finish a piece of work in 4 days. Therefore, to finish one part of work they will take 1/4 days

.....(1)

Similarly, 3 men and 6 boys can finish the same work in 3 days. Therefore, to finish one part of work they will take 1/3 days

.....(2)

Multiplying equation (1) by 3 and equation (2) by 2 and using the elimination method, we have

v = 36

Substituting the value of v in equation (1), we get -

u = 18

Thus, time taken by one man to finish the work alone = 18 days

and, time taken by one boy to finish the work alone = 36 days

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Dealing With the Real Life Problems53 mins
Quiz | Solution of Linear Equations53 mins
Champ Quiz | Consistency and Inconsistency of Solutions36 mins
Pair of Linear Equations in Two Variables46 mins
Smart Revision | Important Word Problems37 mins
Quiz | Real Life Problems Through Linear Equations56 mins
Dealing with the Real Life Problems54 mins
Elimination (quicker than quickest)44 mins
Bonus on Applications of Linear Equations in Two Variables43 mins
Consistent and Inconsistent Equations33 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :