A person sells an item at 15% profit. If she had bought the item at 15% lower price and sold it at Rs. 10.40 less, what would be the purchase price of that item if the item had made 20% profit?
Answers
Answer:
New Cost Price (when price is reduced by 15%) = Rs. 68
Step-by-step explanation:
Let CP be 'x'.
Initially, CP is 'x' and SP is '1.15x' because profit is 15%.
Explanation -
(Profit = SP - CP/CP
=> 15/100 = (SP - x) / x
=> 15x = 100 SP - 100x
=> 115x = 100 SP
=> 115x/100 = SP)
Therefore, SP = 1.15x
Now, information about the second time the seller sold her goods.
1. CP is reduced by 15%, hence, new CP will be 0.85x.
2.SP is reduced by Rs. 10.40 (This point will be used later)
3. Profit made in second transaction is 20%.
To find New CP, we will have to find New SP.
Using : Profit = (SP - CP) / CP
=> 20/100 = (SP - 0.85x) / 0.85x
=> 17x = 100 SP - 85x
=> 102x = 100 SP
=> SP = 1.02 x
Using Point (3) from case 2 :
SP Initial - SP Final = Rs. 10.40
=> 1.15x - 1.02x = Rs. 10.40
=> 0.13x = Rs. 10.40 => x = Rs. 80
We know that CP final was 0.85x hence, 0.85 × 80 = Rs. 68
