Free Class 10 CBSE Mathematics Word problems MCQs with step-by-step solutions (2 questions). Part of Pair of Linear Equations in Two Variables. Practise online on Prepizo — no login needed.
Q1 — Word problems · easy · theory
A student sets up a word problem and gets the equations $3x + 2y = 12$ and $6x + 4y = 24$. Before solving, what does the student notice?
A. The equations are independent and will give different values
B. One equation is a multiple of the other, so they represent the same constraint ✓ Correct
C. The equations are contradictory and have no solution
D. A unique solution exists but must be found by cross-multiplication
Solution: The second equation is exactly $2 \times$ the first equation. This means they represent the same linear relationship, not two different constraints. In the context of a word problem, this often indicates the problem has been stated redundantly, and there are infinitely many solutions (or the problem is under-determined).
Q2 — Word problems · hard · theory
In a word problem, a student solves the system x + y = 50 and 2x + y = 80, finding x = 30, y = 20. What is the critical reasoning step before accepting this solution?
A. Check that both x and y are positive and contextually meaningful (30 items and 20 items make sense) ✓ Correct
B. Verify that the system has infinitely many solutions
C. Confirm that the two equations are parallel
D. Ensure the solution uses only integer coordinates
Solution: Mathematical solutions must be checked against the real-world context. A negative number of items is algebraically valid but contextually impossible. The reasoning connects the abstract solution back to the problem requirements.