Pair of Linear Equations in Two Variables — Question Ex 3.7 Q4
Back to all questionsEx 3.7 Class 10 Maths Question 4.
The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row, there would be 2 rows more. Find the number of students in the class.
Let the number of rows be x and the number of students in each row be y.
Then the total number of students = xy
Case I: When there are 3 more students in each row
Then the number of students in a row = (y + 3)
and the number of rows = (x – 1)
Total number of students = (x – 1) (y + 3)
∴ (x – 1) (y + 3) = xy
⇒ 3x -y =3 …(i)
Case II: When 3 students are removed from each row
Then the number of students in each row = (y-3)
and the number of rows = (x + 2)
Total number of students = (x + 2) (y – 3)
∴ (x + 2) (y – 3) = xy
⇒ -3x + 2y = 6 …(ii)
Adding the equations (i) and (ii), we get
-y + 2y = 3 + 6
⇒ y = 9
Putting y = 9 in the equation (ii), we get
-3x + 18 = 6
⇒ x = 4
∴ x = 4 and y = 9
Hence, the total number of students in the class is 9 x 4 = 36.
CBSE Class 10 Pair of Linear Equations — Complete Guide
This chapter carries 5-6 marks and is crucial for the Algebra unit. Master graphical and algebraic methods for solving pairs of linear equations.
Quick Revision: Key Concepts
- Unique solution: a1/a2 ≠ b1/b2 (intersecting lines)
- Infinite solutions: a1/a2 = b1/b2 = c1/c2 (coincident lines)
- No solution: a1/a2 = b1/b2 ≠ c1/c2 (parallel lines)
- Methods: Substitution, Elimination, Cross-multiplication
- Reducible equations: Substitute u = 1/x, v = 1/y
Most Important Questions
- Determine consistency of a system of equations
- Solve using elimination or substitution method
- Word problems: age, speed, fraction, geometry type
- Equations reducible to linear form (1/x, 1/y type)
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