Find the best tutors and institutes for Class 10 Tuition
Q2(ii):
Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method : (ii) Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?
Solution :
Given:
1. Five years ago, Nuri's age was thrice the age of Sonu.
2. Ten years later, Nuri's age will be twice the age of Sonu.
To Find:
The present ages of Nuri and Sonu.
Step 1: Defining Variables
Let the present age of Nuri be $x$ years.
Let the present age of Sonu be $y$ years.
Step 2: Formulating the Equations
Condition 1: Five years ago
Nuri's age was $(x - 5)$ and Sonu's age was $(y - 5)$.
According to the problem: $(x - 5) = 3(y - 5)$
$x - 5 = 3y - 15$
$x - 3y = -15 + 5$
$x - 3y = -10$ --- (Equation 1)
Condition 2: Ten years later
Nuri's age will be $(x + 10)$ and Sonu's age will be $(y + 10)$.
According to the problem: $(x + 10) = 2(y + 10)$
$x + 10 = 2y + 20$
$x - 2y = 20 - 10$
$x - 2y = 10$ --- (Equation 2)
Step 3: Solving by Elimination Method
We have the system of equations:
(1) $x - 3y = -10$
(2) $x - 2y = 10$
To eliminate $x$, subtract Equation (1) from Equation (2):
$(x - 2y) - (x - 3y) = 10 - (-10)$
$x - 2y - x + 3y = 10 + 10$
$y = 20$
Step 4: Finding the value of $x$
Substitute $y = 20$ into Equation (2):
$x - 2(20) = 10$
$x - 40 = 10$
$x = 10 + 40$
$x = 50$
Step 5: Verification
Five years ago: Nuri was $50 - 5 = 45$, Sonu was $20 - 5 = 15$. Since $45 = 3 \times 15$, the first condition is satisfied.
Ten years later: Nuri will be $50 + 10 = 60$, Sonu will be $20 + 10 = 30$. Since $60 = 2 \times 30$, the second condition is satisfied.
Final Answer: The present age of Nuri is 50 years and the present age of Sonu is 20 years.
More Questions from Class 10 Mathematics Pair of linear equations in two variable EXERCISE 3.3
- Q1(i): Solve the following pair of linear equations by the elimination method and the substitution method : (i) x + y = 5 and 2x – 3y = 4
- Q1(ii): Solve the following pair of linear equations by the elimination method and the substitution method : (ii) 3x + 4y = 10 and 2x – 2y = 2
- Q1(iii): Solve the following pair of linear equations by the elimination method and the substitution method : (iii) 3x – 5y – 4 = 0 and 9x = 2y + 7
- Q1(iv): Solve the following pair of linear equations by the elimination method and the substitution method : (iv) $\frac{x}{2} + \frac{2y}{3} = -1$ and $x - \frac{y}{3} = 3$
- Q2(i): Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method : (i) If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes $\frac{1}{2}$ if we only add 1 to the denominator. What is the fraction?
- Q2(iii): Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method : (iii) The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
- Q2(iv): Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method : (iv) Meena went to a bank to withdraw ` 2000. She asked the cashier to give her ` 50 and ` 100 notes only. Meena got 25 notes in all. Find how many notes of ` 50 and ` 100 she received.
- Q2(v): Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method : (v) A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid ` 27 for a book kept for seven days, while Susy paid ` 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
CBSE Solutions for Class 10 Mathematics Pair of linear equations in two variable
Chapters in CBSE - Class 10 Mathematics
Top Tutors who teach Pair of linear equations in two variable
Top Tutor
Mohkam Pur Kala, Dehradun
8 yrs of
Exp
1 student
Student's Home
Tutor's home
5 years experience in teaching in math and science
Top Tutor
Sector-21, Chandigarh
6 yrs of
Exp
150
per hour
Online Classes
Student's Home
Tutor's home
All the concepts are taught well and doubts are resolved at the earliest. Each student gets personal attention.for in depth knowledge and concept clarity , students of targeted classes may contact. M well experienced, qualified teacher and tutor with over ,6 years of experience in teaching maths and chemistry across different boards including cbse ,icse M a passionate teacher helping hundreds of students to overcome their fear from maths nd chemistry
I am very much thankful to Ravinder sir. My son scored very good score in class 10 under his guidance. Their way of teaching is very impressive and very impactful. Doubts of my child we're cleared on time that's why he was able to complete his syllabus and he was able to get 9.8 CGPA. Their way of teaching is different from other institution in Chandigarh. I would highly recommend all the parents to send their child to excellence academy for their bright future.
Top Tutor
Sultanpur Viran, Sultanpur Viran
9 yrs of
Exp
9 students
1105 hrs of classes completed
1000
per hour
Online Classes
Student's Home
Tutor's home
I have a teaching experience of 9+ years. Currently teaching in St. Mary's Convent School. My way of teaching is simple and friendly as per the requirement. I lay emphasis on the basics because that only helps to make the concepts more easier to understand.
Excellent teacher. He should be given lot of work. Very kind person. He took my daughter from lowest level to 80% in a very short period.
Top Tutor
Jawahar Nagar Sector 5, Jaipur
4 yrs of
Exp
1 student
20 hrs of classes completed
350
per hour
Online Classes
Tutor's home
As a dedicated and experienced educator, I offer personalized class 6 to 10 and till BCA in a supportive online learning environment. With a strong background in Mathematics, Science, and Computers, I am committed to helping students achieve academic excellence and develop a deep understanding of complex concepts. My teaching approach is centered around clarity, simplicity, and innovative methods, ensuring that students of all learning styles feel engaged and motivated. With a proven track record of consistently high academic achievement and a passion for inspiring a love for learning, I am confident in my ability to make a positive impact on my students' academic journeys.
Avdesh sir tailored the lessons to meet my individual needs, making complex topics accessible and engaging.
Top Tutor
Bataganj, Patna Sadar
2 yrs of
Exp
100
per hour
Online Classes
I am an experienced Spoken English and Class VI-X subject tutor with two years of experience in teaching. Currently, I am pursuing my bachelor's degree in BA from Magadh University. I can teach students who are in State, International Baccalaureate, CBSE and ICSE Board. My students have improved a lot through my teaching, and I've received five reviews till now with 100% positive feedback. I always try to understand my students and help them overcome their fear of failure in specific subjects like math and science.
Find more Tutor for Pair of linear equations in two variable in your City
- Bangalore Mathematics Tutors
- Delhi Mathematics Tutors
- Chennai Mathematics Tutors
- Gurgaon Mathematics Tutors
- Noida Mathematics Tutors
- Hyderabad Mathematics Tutors
- Mumbai Mathematics Tutors
- Ghaziabad Mathematics Tutors
- Chandigarh Mathematics Tutors
- Pune Mathematics Tutors
- Jaipur Mathematics Tutors
- Surat Mathematics Tutors
Download free CBSE - Class 10 Mathematics Pair of linear equations in two variable EXERCISE 3.3 worksheets
Download Now
