A seller decreased the selling price of each item from ₹5,000 to ₹4,680, by which his loss percentage increased by 4%. If he has to get 4% profit, then the selling price of the item should be:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. ₹8,320.
Let's denote:
CP as the cost price of the item.
SP1 as the initial selling price (₹5,000).
SP2 as the new selling price (₹4,680).
We know that:
⇒ Initial loss% = (CP - SP1) / CP × 100
⇒ New loss% = (CP - SP2) / CP × 100
We are also given that the new loss percentage is 4% more than the initial loss percentage:
⇒ (CP - SP2) / CP × 100 = (CP - SP1) / CP × 100 + 4
Substituting the values of SP1 and SP2:
⇒ (CP - 4680) / CP × 100 = (CP - 5000) / CP × 100 + 4
Simplifying the equation:
⇒ 100CP - 468000 = 100CP - 500000 + 4CP
⇒ 4CP = 32000
⇒ CP = 8000
Now, to achieve a 4% profit, the selling price (SP3) should be:
⇒ SP3 = CP × (1 + Profit%)
⇒ SP3 = 8000 × (1 + 0.04)
⇒ SP3 = 8320
Therefore, the selling price of the item should be ₹8,320 to achieve a 4% profit.