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In the ninety-nine shop every item costs some whole number of rupees plus 99 paise. Rhea spent sixty five rupees and seventy six paise in buying some items from the shop. How many items did she buy?
If she buys $$n$$ items, the paise contribution is $$99n$$ paise. Since the total is $$65.76$$ rupees, $$99n$$ must be at most $$6576$$ paise and must end in $$76$$ paise. The congruence $$99n\equiv76\pmod{100}$$ gives $$n=24$$ within this range, and $$24\times99=2376$$ paise leaves $$42$$ rupees for the whole rupee parts.
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