A shopkeeper mark up price of LED 60% above its cost price and gives t...
Let's denote the cost price of the LED as CP, the marked up price as MP, and the selling price after three successive discounts as SP.
The marked up price (MP) is 60% above the cost price (CP), so:
MP = CP + 0.60 * CP
MP = 1.60 * CP
The shopkeeper gave three successive discounts of 12.5%, d%, and 25%. Therefore, the selling price (SP) can be calculated as follows:
SP = MP * (1 - 0.125) * (1 - d/100) * (1 - 0.25)
We know that the shopkeeper incurred a loss of 16%. To find the loss percentage, we can use the formula:
Loss Percentage = ((CP - SP) / CP) * 100
Given that the loss percentage is 16%, we can substitute this into the equation and solve for SP:
16 = ((CP - SP) / CP) * 100
(CP - SP) / CP = 16/100
CP - SP = 0.16 * CP
SP = CP - 0.16 * CP
SP = 0.84 * CP
Now, we can substitute the expression for SP from step 3 into the equation for SP in step 2:
0.84 * CP = 1.60 * CP * (1 - 0.125) * (1 - d/100) * (1 - 0.25)
Simplify the equation:
0.84 = 1.60 * 0.875 * (1 - d/100) * 0.75
Further simplify:
0.84 = 1.05 * (1 - d/100)
Divide both sides by 1.05:
0.8 = 1 - d/100
Solve for d:
d/100 = 1 - 0.8
d/100 = 0.2
d = 0.2 * 100
d = 20%
So, the second discount allowed by the shopkeeper is 20%.