Two schools 'P' and 'Q' decided to award prizes to their students for two games of Hockey ₹ x per student and Cricket ₹ y per student. School 'P' decided to award a total of ₹ 9,500 for the two games to 5 and 4 students respectively; while school 'Q' decided to award ₹ 7,370 for the two games to 4 and 3 students respectively.
Generated by claude-sonnet-4-6 · 2026-06-15 10:33 · grounding stimulus
Model Answer
(i) The two equations are:
School P: $5x + 4y = 9500$
School Q: $4x + 3y = 7370$
(ii) Solving the equations:
Multiply eq.1 by 3 and eq.2 by 4:
$15x + 12y = 28500$
$16x + 12y = 29480$
Subtracting: $x = 980$
Substituting in eq.1: $5(980) + 4y = 9500 \Rightarrow 4y = 4600 \Rightarrow y = 1150$
Prize amount for Hockey = ₹ 980
OR Cricket prize (₹1150) > Hockey prize (₹980); Cricket is more by ₹170.
(iii) Total prize amount for 2 students each:
$= 2x + 2y = 2(980) + 2(1150) = 1960 + 2300 =$ ₹ 4,260
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Explanation
- (i) Just frame the linear equations — 1 mark for both equations correct.
- (ii) Either find x (Hockey prize) OR compare x and y — both valid options. Show elimination/substitution steps clearly.
- (iii) Substitute found values into $2x + 2y$. Carry-forward marks apply if arithmetic error in (ii).
- Key values: x = ₹980 (Hockey), y = ₹1150 (Cricket).