Introduction to Discount and Marked Price for RRB Exams

In the competitive landscape of Indian Railway Recruitment Board (RRB) exams, the arithmetic section plays a pivotal role in determining a candidate's success. Within the profit and loss module, 'Discount and Marked Price' is a high-frequency topic. Understanding the relationship between the Cost Price (CP), Selling Price (SP), and Marked Price (MP) is essential for solving these problems quickly and accurately.

Topic Weightage and Importance

In both RRB NTPC and Group D examinations, arithmetic forms nearly 30-40% of the quantitative aptitude section. You can consistently expect 1 to 2 questions specifically focused on discount calculations. Mastering this topic allows you to secure easy marks within seconds, which is crucial for maintaining time efficiency during the actual test.

Key Concepts and Formulas

To master this topic, you must familiarize yourself with these core definitions and formulas:

  • Marked Price (MP): The price printed on the tag of an item (also known as the List Price).
  • Discount: The reduction offered on the Marked Price. Discount = MP - SP.
  • Discount Percentage: (Discount / MP) × 100.
  • Selling Price (SP): SP = MP - Discount.
  • Relationship Formula: SP = MP × (100 - Discount%) / 100.
  • Combined Profit/Discount Formula: MP / CP = (100 + Profit%) / (100 - Discount%).

Solved Examples (Step-by-Step)

Example 1: An item marked at ₹800 is sold at a 15% discount. Find the selling price.

Step 1: Identify MP = 800, Discount = 15%.
Step 2: Calculate Discount amount = 15% of 800 = (15/100) * 800 = ₹120.
Step 3: SP = MP - Discount = 800 - 120 = ₹680.

Example 2: A shopkeeper marks his goods 20% above cost price and allows a 10% discount. Find his gain percentage.

Step 1: Let CP = 100. Then MP = 120.
Step 2: Discount = 10% of 120 = 12.
Step 3: SP = 120 - 12 = 108.
Step 4: Gain% = ((SP - CP) / CP) * 100 = ((108 - 100) / 100) * 100 = 8%.

Common Mistakes to Avoid

  • Calculating discount percentage on Cost Price instead of Marked Price.
  • Forgetting to convert percentages to absolute values before subtracting.
  • Assuming that adding two successive discounts (e.g., 10% and 20%) equals a 30% discount; always use the formula: A + B - (AB/100).
  • Misreading the question when it asks for the 'Marked Price' instead of the 'Selling Price'.

Practice Questions with Solutions

  1. If MP is ₹1200 and SP is ₹1050, what is the discount %? (Ans: 12.5%)
  2. A single discount equivalent to a discount series of 20% and 10% is? (Ans: 28%)
  3. An article is marked at 40% above CP. If it is sold at a 10% discount, what is the profit %? (Ans: 26%)
  4. By selling an item for ₹450 after a 10% discount, what was the MP? (Ans: ₹500)
  5. A trader marks his goods at 25% above CP. If he wants a 5% profit, what discount % should he offer? (Ans: 16%)

Frequently Asked Questions (FAQs)

Q1: Is Discount always calculated on MP? Yes, unless stated otherwise in the problem statement.

Q2: How do I handle successive discounts? Use the formula (1 - d1/100) * (1 - d2/100) * MP = Final Price.

Q3: Can I skip this topic? Not recommended. It is one of the easiest ways to gain marks in the RRB math section.

Conclusion and Final Tips

Discount problems are essentially variations of percentage problems. Practice calculating mental percentages to save time. Focus on the relationship between CP, MP, and SP, and you will find these problems to be very scoring. Stay consistent, practice daily, and you will surely ace your RRB exam!