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Akshita bought a digital watch and sold it to Ravi at 25% profit. Ravi sells the same watch to Sweta at 30% loss at the price of Rs. 4550. Find the price at which Akshita bought the watch.  
1. Rs. 5200
2. Rs. 4700
3. Rs. 6500
4. Rs. 4900

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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.

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