This question appeared in Aryabhatta Inter School Maths Competition 2020
Tejaswini is baking muffins. When she packs 3 muffins in a box, 2 muffins are left. If she packs 5 muffins in a box, 3 muffins are left. When she packs 7 muffins in a box, she is left with as many muffins as were left when she packed 5 muffins. What was the least number of muffins she baked ?
Answer is : 38
This question can also be solved using Euclid's division lemma, as follows:
By the given conditions, we can express the total number of muffins $K$ as, $$K=3a+2=5b+3=7c+3$$ where $a,b,c$ are the number of boxes packed fully.
Hence, $$K-3=5b=7c$$ which means that $K-3$ is a multiple of both $5$ and $7$. The smallest number to exhibit this property is obviously: $$LCM(5,7)=35$$ Hence, $$K-3=35 \implies K=38$$ However, we cannot be sure it is a correct answer until and unless it satisfies the other condition too, now $$38=3(12)+2$$ Hence, our answer is $ 38$.