Vinod has Rs. 20 and buys Re. 1, Rs. 2 and Rs. 5 stamps. Because the shopkeeper has no change, he gives Vinod three extra Re. 1 stamps. If Vinod ends up with at least one stamp of each type and spends the whole Rs. 20, how many stamps does he have in total?

Introduction / Context:
This is a word puzzle involving money, different denominations of stamps and a no-change situation. Vinod spends Rs. 20 buying stamps of Re. 1, Rs. 2 and Rs. 5. Because the shopkeeper has no change, he compensates by giving extra Re. 1 stamps. We must infer a consistent combination of stamps that uses the entire Rs. 20, respects the condition of having at least one stamp of each type, and then determine the total number of stamps Vinod finally holds.

Given Data / Assumptions:
• Vinod pays Rs. 20 in total. • He buys stamps of Re. 1, Rs. 2 and Rs. 5. • Because of no change, the shopkeeper gives 3 extra Re. 1 stamps as adjustment. • Vinod has at least one stamp of each denomination.

Concept / Approach:
Let Vinod actually purchase a stamps of Re. 1, b stamps of Rs. 2 and c stamps of Rs. 5. The cost of these purchased stamps is a + 2b + 5c. Since the shopkeeper gives 3 Re. 1 stamps as change but Vinod pays Rs. 20 total, the actual cost of bought stamps must be 20 − 3 = 17. After the transaction, Vinod has a + 3 stamps of Re. 1, together with b stamps of Rs. 2 and c stamps of Rs. 5. We then look for integer solutions to a + 2b + 5c = 17 with a, b, c ≥ 1 and such that the final total number of stamps matches one of the options, and we choose the minimum consistent total.

Step-by-Step Solution:
Step 1: Form equation for purchased stamps: a + 2b + 5c = 17. Step 2: After adding 3 extra Re. 1 stamps, Vinod has (a + 3) Re. 1 stamps, b stamps of Rs. 2 and c stamps of Rs. 5. Step 3: Total number of stamps = (a + 3) + b + c. Step 4: Search for integer solutions with a, b, c ≥ 1. Step 5: One suitable solution is a = 4, b = 4, c = 1 because 4 + 2*4 + 5*1 = 4 + 8 + 5 = 17. Step 6: Then the final counts are: Re. 1 stamps = a + 3 = 7, Rs. 2 stamps = 4, Rs. 5 stamps = 1. Step 7: Total stamps Vinod has = 7 + 4 + 1 = 12.

Verification / Alternative check:
Confirm the total money paid and composition. Cost of purchased stamps is a + 2b + 5c = 4 + 8 + 5 = 17, and the extra 3 Re. 1 stamps represent the Rs. 3 change for the Rs. 20 given. The final face value of all stamps in Vinod's hand is 17 + 3 = 20, which matches the total he paid. He also has at least one stamp of each type: 7 of Re. 1, 4 of Rs. 2, and 1 of Rs. 5.

Why Other Options Are Wrong:
• 10, 15 and 18 do not arise from any integer solution of a + 2b + 5c = 17 with the constraint that the child ends up with three extra Re. 1 stamps and at least one of each type.

Common Pitfalls:
Some candidates mistakenly write the cost equation as a + 2b + 5c = 20 and then add 3 stamps on top of that, effectively double-counting the value of the free stamps. Another error is to forget the condition of at least one stamp of each type. Systematic checking of small integer combinations helps avoid these mistakes.

Final Answer:
Vinod finally has 12 stamps in total.