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Prachi sold a table for Rs. 625 at some profit. Had she sold it for Rs. 475, then there would have been a loss equal to one-fifth of the initial profit. Which of the following is correct?

A. CP < first SP – 100

B. CP > Second SP

C. 500 < CP < 600

D. CP ≤ 4 × 53


1. A and B
2. A, B, and D 
3. B, C, and D
4. Only C

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Correct Answer - Option 2 : A, B, and D 

Given:

First SP = Rs. 625

Second SP = Rs. 475

Loss = (1/5)Profit

Formula Used:

Profit = SP – CP

Loss = CP – SP

Where CP is cost price and SP is selling price.

Calculation:

Profit = 625 – CP

Loss = CP – 475

Loss = (1/5)Profit

⇒ CP – 475 = 1/5(625 – CP)

⇒ CP – 475 = 125 – (1/5)CP

⇒ (6/5)CP = 600

⇒ CP = 600 × 5/6

⇒ CP = 500

CP = Rs. 500

A. CP < first SP – 100

first SP – 100 = 625 – 100

⇒ 525

⇒ CP = 500 < 525

⇒ A is correct

B. CP > Second SP

500 > 475

⇒ B is correct

C. 500 < CP < 600

CP = Rs. 500

⇒ 500 = CP < 600

⇒ C is incorrect

D. CP ≤ 4 × 53

⇒ CP = 500

⇒ 4 × 125

⇒ 4 × 53

⇒ D is correct

A, B, and D are correct

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