Introduction

The given problem involves determining the marked price of a watch based on the differences in discount levels offered by a shopkeeper. The problem presents several different approaches to solving the same issue, highlighting the consistency and reliability of the principle involved.

Problem Statement

A shopkeeper offers a discount of 5% on a watch, but when the discount is increased to 7%, he earns Rs. 15 less as profit. This article will guide us through calculating the marked price of the watch based on the difference in discount levels and the resulting profit difference.

Approach 1: Using Initial Values

Let the marked price be 100.
Discount 5 (100 x 95/100) 95
Discount 7 (100 x 93/100) 93
Difference in selling price 95 - 93 2
When 2 is equal to Rs 30
100 is equal to 1500
Marked price Rs 1500

Approach 2: Allowing for Proportions

Marked price includes discount
2 (7-5 in discount amounts) to Rs 30
100 of discount or marked price 1500

Approach 3: Using Algebraic Equations

Let the marked price is Rs 100.
The difference between the two discounts 7 - 5 Rs 2.
So, we can say that the profit will be less by Rs 2 when the marked price is Rs 100.
Therefore, if the difference is Rs 30, the marked price is Rs 100 × 30/2 Rs 1500.

Approach 4: Calculating Using Ratios

Let the marked price of the watch be Rs.100.
The difference in the discount 7 - 5 Rs.2.
If the difference is Rs.2, the MP Rs.100.
If the difference is Rs.30, the MP 100 × 30/2 Rs 1500.

Approach 5: Simplifying the Calculation

The problem indicates that there is a change in the discount on the marked price - by allowing a discount of 5 to 7, the profit is less by Rs. 30 i.e., the discount increased by Rs. 30.
So, 7 - 5 2 discount on the marked price Rs.30.
Therefore, the marked price 30 / 2 30 × 100 / 2 Rs. 1500 Ans.

Approach 6: Using a Direct Proportion Method

Let the marked price be 10.
5 discount sale price 95x
7 discount sale price 93x
95x - 93x 30
x 15
10 Rs 1500 ANS

Approach 7: Incorrect Application of the Principle

Let the Marked Price be 100. Discount 15. Selling Price 85 of MP.
When discount allowed is 20, the SP becomes 80 of MP.
Difference 5 which is equal to 5/5 of MP
Therefore, MP 100 × 5/5 1020/-
Hence, the original marked price of the watch is Rs.1020/-

Conclusion

Regardless of the method employed, the marked price of the watch is consistently calculated to be Rs.1500 based on the difference in discount levels and the resulting profit difference. This problem highlights the importance of understanding the principle of discounts and their impact on the overall profit structure.