One of the most important and conceptual question from linear equations in two variables in which we have given that 2 men and 5 boys together can finish a piece of work in 4 days, while 3 men and 6 boys can finish it in 3 days. We have to find the time taken:
i) by one man alone to finish the work
ii) by one boy alone to finish the work.
Kindly give me a detailed solution of this question
RS Aggarwal, Class 10, chapter 3E, question 37
Let the amount of work done by a Man alone in a day be M and by a Boy alone be B
Given, 2 men and 5 boys together can finish a piece of work in 4 days
Amount of work they can do in one day 2M+5B =1/4 — (1)
Similarly, 3M+6B=1/3 — (2)
Solving equations (1) and (2), we get B=1/36
Substituting B in equation (2), we get M=1/18
Hence, one man alone will take 18 days to do the work and one boy will take 36 days.