Correct Answer - Option 4 : Rs. 2880
Given:
Cost price of both racks = Rs. 5200
Profit on first rack = 16%
Loss on second rack = 10%
Formula Used:
Profit % = ((SP - CP)/CP) × 100%
Loss % = ((CP - SP)/CP) × 100%
Calculation:
Let the cost price of first rack = Rs. x
and the cost price of second rack = Rs. y
Profit on first rack = 16%
Profit % = ((SP - CP)/CP) × 100%
⇒ 16 = ((SP - x)/x) × 100
⇒ 16x = 100(SP - x)
⇒ 16x = 100SP - 100x
⇒ 116x = 100SP
SP = (116/100)x
Loss on second rack = 10%
Loss % = ((CP - SP)/CP) × 100%
⇒ 10 = ((y - SP)/y) × 100
⇒ 10y = 100(y - SP)
⇒ 10y = 100y - 100SP
⇒ 100SP = 90y
SP = (90/100)y
∵ There is no gain or loss
Cost price of first rack + Cost price of second rack = Selling price of first rack + Selling price of second rack
⇒ x + y = (116/100)x + (90/100)y
⇒ 16x = 10y
⇒ x = (10/16)y
∵ x + y = 5200
⇒ (10/16)y + y = 5200
⇒ (26/16)y = 5200
⇒ y = 3200
SP of second rack = (90/100)y
SP of second rack = (90/100) × 3200
SP of second rack = Rs.2880
∴ The selling price of the rack sold at loss is Rs.2880.