Class 9 Maths Chapter 13 | Questions 10–16 | Full NCERT Solutions | Two Variables, One Line

End-of-Chapter Exercises of Ganita Manjari Part II 📘 Class 9 Maths Chapter 13 – Two Variables, One Line Welcome to the complete question-solving session for Questions 10 to 16 from the End-of-Chapter Exercises of Ganita Manjari Part II. In this video, we cover coincident lines, intersecting paths, number puzzles, cyclic quadrilaterals, train-speed problems, and age-related word problems using linear equations. *Question 10:* Find the value of ‘k’ for which the following system of equations represents a pair of coincident lines: x + 2y = 3; (k – 1)x + (k + 1)y = k + 3. *Question 11:* (i) Robot 1 starts from the origin and traces a path by repeatedly moving 3 units to the right and then 4 units upward. Robot 2 starts from the point (10, 0) and repeatedly moves 1 unit to the right and then 2 units upward. Will the paths traced by these two robots intersect and if so, where? (ii) Robot 1 starts from (3, 0) and traces a path by repeatedly moving 5 units to the right and then 5 units upward. Robot 2 starts from the point (7, 0) and repeatedly moves 5 units to the right and then 3 units downwards. Will the paths traced by these two robots intersect and if so, where? *Question 12:* At a certain time, Jacob notices that his digital watch reads ‘a’ minutes after two o’clock. Fifteen minutes later, it reads ‘b’ minutes after three o’clock. He noticed that a is six times greater than b. What time was it when he looked at his watch for the second time? *Question 13:* The sum of the digits of a two-digit number is 15. The number obtained by interchanging the digits exceeds the given number by 9. Find the number. *Question 14:* In a cyclic quadrilateral ABCD, ∠A = (x + 7)°, ∠B = (y + 8)°, ∠C = (3y + 23)° and ∠D = (4x + 12)°. Find all four angles of the cyclic quadrilateral. *Question 15:* A train moving with uniform speed for a certain distance takes 6 hours less if its speed is increased by 6 km/hour. It would have taken 6 hours more had its speed been decreased by 4 km/hour. Find the distance travelled and the speed of the train. *Question 16:* The age of a father is equal to the sum of the ages of his four children. After 20 years, the sum of the ages of the children will be twice the age of the father. Find the age of the father. 📌 *Topics covered:* • Coincident lines and linear equations • Intersecting paths and graphs • Forming equations from word problems • Number puzzles and digit interchange • Angles of a cyclic quadrilateral • Train speed, time and distance • Age-related problems 📚 Class 9 Mathematics | Chapter 13 – Two Variables, One Line 📖 Ganita Manjari Part II | End-of-Chapter Exercises 👍 Like the video if it helps you understand the concepts. 🔔 Subscribe for more Class 9 Maths solutions and chapter-wise explanations. #Class9Maths #NCERTSolutions #MathsChapter13 #LinearEquations #TwoVariablesOneLine #GanitaManjari