Q&A -Ask Doubts and Get AnswersPrevious Next
Pair of linear equations in two variables CBSE NCERT Solutions
Formulate the following problems as a part of equations, and hence find their solutions.
(i) Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current.
(ii) 2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.
(iii) Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.
(i) Let the speed of rowing in still water is x km/h
Let the speed of current is y km/h.
So, the speed of rowing downstream is (x + y) km/h.
And, the speed of rowing upstream is (x − y) km/h.
According to given conditions,
⇒ 2x + 2y = 20 and 2x − 2y = 4
⇒ x + y = 10 … (1) and x – y = 2 … (2)
Adding equation (1) and equation (2), we get
2x = 12
⇒ x = 6
Putting x = 6 in equation (1), we get
6 + y = 10
⇒ y = 10 – 6 = 4
Therefore, the speed of rowing in still water is 6 km/h and the speed of the current is 4 km/h.
(ii) Let the time taken by 1 woman alone to finish the work in x days
and the time is taken by 1 man alone to finish the work in y days.
So, 1 woman’s 1-day work = part of the work.
And, 1 man’s 1-day work = part of the work.
So, 2 women’s 1-day work = part of the work
And, 5 men’s 1-day work = part of the work.
Therefore, 2 women and 5 men’s 1-day work = part of the work… (1)
It is given that 2 women and 5 men complete work in 4 days
It means that in 1 day, they will be completing part of the work … (2)
We can say that equation (1) is the same as (2).
Similarly, … (4)
Let 1/x = p and 1/y = q
Putting 1/x = p and 1/y = q in equation (3) and equation (4), we get
⇒ 8p + 20q = 1 … (5) and 9p + 18q = 1 … (6)
Multiplying equation (5) by 9 and equation (6) by 8, we get
72p + 180q = 9 … (7)
72p + 144q = 8 … (8)
Subtracting (8) from equation (7), we get
36q = 1
⇒ q = 1/36
Putting the value of q = 1/36 in equation (6), we get
⇒ 9p = 1/2
⇒ p = 1/18
Putting values of p = 1/18 and q = 1/36 in respectively, we get x = 18 and y = 36
Therefore, 1 woman completes work in 18 days.
And, 1 man completes work in 36 days.
(iii) Let the speed of the train is x km/h and the speed of the bus is y km/h
According to given conditions,
Let 1/x = p and 1/y = q
Putting this in the above equations, we get
60p + 240q = 4 … (1)
And 100p + 200q = … (2)
Multiplying equation (1) by 5 and equation (2) by 3, we get
300p + 1200q = 20 … (3)
300p + 600q = … (4)
Subtracting equation (4) from equation (3), we get
600q = 20 − = 7.5
⇒ q =
Putting the value of q in (2), we get
⇒ p =
But 1/x = p and 1/y = q
Therefore, x = 600/10 = 60 km/h and y = 600/7.5 = 80 km/h.
Therefore, the speed of the train is 60 km/h and the speed of the bus is 80 km/h.
Related Questions for Study
What our students and parents say about us!
Saiyam is using EduSaksham online courses from past one year. He is able to complete his tutorials, worksheets, and assignments on his own. Once he is done with worksheets, he can check his answers and if he has done any mistakes, then he can check the correct answers and explanations. They have been given so well that he is able to understand them himself and rarely he asks us for any clarification. He enjoys using the platform and has learned and improved a lot in Mathematics. I would recommend EduSaksham to all parents who want their kids to learn in a structured way and also enjoy the learning process.
Neeraj (Saiyam's Father)
I would like to thank Edusaksham on behalf of my son Aditya who attended " Math Olympiad crash course for 5 weeks". As per Aditya, this course helped him to understand new topics like Roman numerals and decimal places which were not taught in his school till date and had a better understanding of other topics. I personally thank EduSaksham for all the help and support.
Geeta Bansal (Aditya's Mother)
We had a good experience with EduSaksham. Because sheets are available online, Vedant enjoyed doing more and more sheets without any reminders. I could leave him on his own as he was very much motivated to cover the topics. Practice is very important in maths but it becomes difficult for us to prepare sheets, I am glad we found EduSaksham where in a lot of in a lot of sheets are available for practice and the quality of questions are also good. As it's a venture from IITians we could think of giving it a try and I am glad we tried
Shikha Chowdhary (Vedant's Mother)
I have grown up in a family where my father used to give me practice maths paper every day which I need to finish before I go to play. I think that strong foundation of solving new questions every day helped me to clear my IITJEE exam. But as working women, I always had time challenge to create practice Math papers for my daughter. Thanks to EduSaksham, their questions are so logical and conceptual that I don't feel the guilt of not creating practice questions by myself :). There are plenty of worksheet along with the tutorials for each chapter. It has made parents life easier :) And the best part is my daughter loves doing it. Thank you EduSaksham.