Step 1: Understand the Equivalent Discount Concept
A single equivalent discount of 31.6% means that after all discounts are applied, the final price is 100% - 31.6% = 68.4% of the original price.
Step 2: Formulate the Equation
Let the original price be 100. The successive discounts are p%, (p/2)%, and (p/4)%. The formula for the final value is:
100 × (1 - p/100) × (1 - p/200) × (1 - p/400) = 68.4
Step 3: Test Option 2 (p = 20)
In competitive exams, testing options is often the fastest method. Let's try p = 20:
- First Discount: p% = 20% (Multiplier = 0.8)
- Second Discount: p/2% = 20/2 = 10% (Multiplier = 0.9)
- Third Discount: p/4% = 20/4 = 5% (Multiplier = 0.95)
Step 4: Verify the Calculation
Calculate the final multiplier:
Final Multiplier = 0.8 × 0.9 × 0.95
= 0.72 × 0.95
= 0.72 × (1 - 0.05)
= 0.72 - 0.036
= 0.684
Now, calculate the single equivalent discount:
Equivalent Discount = (1 - 0.684) × 100 = 31.6%
This matches the value given in the question perfectly.
The value of p is 20%. (Option 2)
Important Questions from Discount and MP
If a trader marks the price of an article 50 percent more than the cost price and allows a discount of 30 percent, then what is his profit percentage?
What will be the selling price of an article if two successive discounts of 15% and 12% are offered on its marked price of Rs. 25,500?
Printed price of a mobile is Rs. 6,400. It is sold in Rs. 2,560 with two consecutive discount. If first discount is 20%, then what is the second discount?
Lekhana saves Rs. 15 on the purchase of a book when a discount of 20% is given. How much did she pay for the book?
Marked price of an article is Rs.4000. Selling price of the article is Rs.2600. What is the discount percentage?
