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?
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?
A trader decided to mark his goods 15 percent above the cost price and then offered 40 percent discount. What will be the percentage of profit or loss?
On the sale of 20 percent discount, the value of an item is Rs. 760. What was the real value of the item?
What is the total discount applicable if 3 successive discounts of 20%, 10% and 12.5% are applied?
