What is the least number of coins required to make one rupee from different coins of 1, 5,...
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What is the least number of coins required to make one rupee from different coins of 1, 5, 10 and 25 paise, so that you have at least one coin of each type?
Show answer & explanation
To make 100 paise with at least one of 1, 5, 10, 25 paise, the 1 paise coins must sum to a multiple of 5 (minimum 5 coins). The remaining 95 paise is made with one 10p, two 5p, and three 25p coins (6 coins), totaling 5 + 6 = 11 coins.
Step-by-step Derivation:
Step 1: Denominations 5, 10, and 25 are multiples of 5, so the number of 1-paise coins must be a multiple of 5 to reach 100 paise.
Step 2: With at least one 1-paise coin, minimum number of 1-paise coins is 5 (5 paise).
Step 3: Remaining amount = 100 - 5 = 95 paise.
Step 4: To minimize total coins using at least one 5p, 10p, 25p: take three 25p (75p), one 10p (10p), and two 5p (10p) => 3 + 1 + 2 = 6 coins.
Step 5: Total coins = 5 + 6 = 11 coins.