Methodology

To find the smallest total number of coins, we need to find the minimum number of coins required to pay each of the three amounts separately. The strategy for finding the minimum number of coins for a given amount is to use the largest denomination coins as much as possible.

The available coin denominations are: 50, 25, 10, 5, and 2 paise.

1. Coins for 78 Paise

We break down 78 paise using the largest coins first:

• Use one 50p coin. Remaining amount: 78 - 50 = 28 paise.
• Use two 10p coins. Remaining amount: 28 - 20 = 8 paise.
• Use four 2p coins. Remaining amount: 8 - 8 = 0.

Total coins = 1 (50p) + 2 (10p) + 4 (2p) = 7 coins.

2. Coins for 66 Paise

We break down 66 paise using the largest coins first:

• Use one 50p coin. Remaining amount: 66 - 50 = 16 paise.
• Use one 10p coin. Remaining amount: 16 - 10 = 6 paise.
• Use three 2p coins. Remaining amount: 6 - 6 = 0.

Total coins = 1 (50p) + 1 (10p) + 3 (2p) = 5 coins.

3. Coins for Rs. 1.01 (101 Paise)

We break down 101 paise using the largest coins first:

• Use one 50p coin. (Using two 50p coins would leave 1p, which is impossible to pay). Remaining amount: 101 - 50 = 51 paise.
• Use one 25p coin. Remaining amount: 51 - 25 = 26 paise.
• Use two 10p coins. Remaining amount: 26 - 20 = 6 paise.
• Use three 2p coins. Remaining amount: 6 - 6 = 0.

Total coins = 1 (50p) + 1 (25p) + 2 (10p) + 3 (2p) = 7 coins.

Total Number of Coins

The smallest total number of coins is the sum of the minimum coins required for each payment:

Total = (Coins for 78p) + (Coins for 66p) + (Coins for 101p)

Total = 7 + 5 + 7 = 19