A medium question on surplus and shortage for P3–P4, with a step-by-step solution, diagrams and the answer. Surplus-and-shortage questions appear in the Hua Xia Cup's P1 to P5 papers; harder ones become questions about distance and time.
The question
A teacher shares out some pencils equally among the class.
With 2 each there are 11 left over; with 5 each there are 19 too few.
How many pupils are in the class?
Show the hints (2)
💡Hint 1: Going from 2 each to 5 each, how many more does each pupil get?
💡Hint 2: From 11 over to 19 short — how many more pencils does that take in all?
Worked solution
Have a go first, then read the solution step by step.
1.With 2 each, 11 are left over.
2.With 5 each, every pupil gets 5 − 2 = 3 more, and there are 19 too few.
3.Where do the extra ones come from? The 11 spare, and 19 more still needed: 11 + 19 = 30 extra in all.
4.At 3 more each, there are 30 ÷ 3 = 10 pupils.
⚠️Common mistake: working out 19 − 11. One is over and one is short, so add them.
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