Correct Answer - Option 1 : Rs. 5200
Given:
Profit at which Akshita sells the watch = 25%
Loss at which Ravi sells the watch = 30%
Price at which Ravi sells the watch = Rs. 4550
Concept Used:
Cost price is always 100%.
Formula Used:
Profit% = (SP - CP)/CP × 100
Loss% = (CP - SP)/CP × 100
where CP → Cost Price, SP → Selling Price
Calculations:
Profit at which Akshita sells the watch = 25%
⇒ CP1 : SP1 : Profit = 4 : (4 + 1) : 1 [25% = 1/4]
⇒ CP1 : SP1 = 4 : 5 ----(1)
Loss at which Ravi sells the watch = 30%
⇒ CP2 : SP2 : Loss = 10 : (10 - 3) : 3 [30% = 3/10]
⇒ CP2 : SP2 = 10 : 7
Price at which Akshita sells and price at which Ravi buys must be same
⇒ Multiplying (1) by 2, we get
CP1 : SP1 = (4 : 5) × 2 = 8 : 10
⇒ Ratio of cost price for Akshita, Ravi and Sweta = 8 : 10 : 7
Price at which Ravi sells and and price at which Sweta buys must be same
Price at which Ravi sells the watch = Rs. 4550
⇒ 1 unit = Rs. 4550/7 = Rs. 650
⇒ Price at which Akshita bought the watch = Rs. 650 × 8 = Rs. 5200
∴ The price at which Akshita bought the watch is Rs. 5200.