Question

Re $ 1 $ and Rs $ 5 $ coins are available (as many as required). Find the smallest payment which cannot be made by these coins, if not more than $ 5 $ coins are allowed.

Answer 1

Hint: In the given problem, we are provided with as many Re $ 1 $ and Rs $ 5 $ coins as required. So, we have to find the smallest amount of payment that cannot be made with the help of the coins in the given denominations, if not more than $ 5 $ coins are allowed in the transaction. Such questions require analytical and critical thinking to get to the correct answer. There can be many amounts that cannot be paid using not more than five coins of denominations Re $ 1 $ and Rs $ 5 $ , but we will look out for the smallest payment only.

Complete step by step solution:
Now, we have the coins in the denominations of Re $ 1 $ and Rs $ 5 $ only.
So, we need to find out the smallest payment that cannot be made by these coins, if not more than five coins are allowed in the transaction.
Hence, we can easily figure out that if we put five coins of Rs $ 5 $ together, then we will only be able to pay Rs $ 25 $ at most.
So, no matter what we try, we will not be able to pay any amount greater than rupees $ 25 $ in the denominations of Re $ 1 $ and Rs $ 5 $ , if only five coins are allowed in the transaction. But, we have to find the least payment that can be made.
So, our final answer has to be less than $ 25 $ rupees.
Now, by hit and trial method, we see that there is only one way to pay the amount of rupees $ 13 $ using the coins of denominations Re $ 1 $ and Rs $ 5 $ , when only five coins are allowed.
So, $ 13 = 5 + 5 + 1 + 1 + 1 $ .
Hence, we can foresee that $ 13 = 5 + 5 + 1 + 1 + 1 + 1 $
Therefore, the amount of rupees $ 14 $ cannot be paid when only five coins are allowed in transactions in the denominations of Re $ 1 $ and Rs $ 5 $ .
Hence, the smallest payment which cannot be made by Re $ 1 $ and Rs $ 5 $ coins, if not more than $ 5 $ coins are allowed in $ 14 $ rupees.
So, the correct answer is “14”.

Note: Such questions require innovative thinking to find out the exact method that leads us to the right answer. A variety of techniques and methods may be used to solve the same problem in different ways but the answer would remain the same as the core principle behind the logic would remain unchanged.