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An article is sold at Rs. n. If it is sold at 70% of this price, there would be a loss of 19.5%. Which of the following is correct?

I. If original selling price is Rs. 920, the cost price is Rs. 800

II. Original selling price is 12% more than cost price

III. If cost price is Rs. 850, n will be Rs. 977.5


1. Only I
2. II and III
3. I and III 
4. None of these

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Correct Answer - Option 3 : I and III 

Given:      

SP1 = Rs. n

SP2 = 70% of n

Loss = 19.5%                      

Formula Used:

Profit% = (Profit/CP) × 100

SP = {(100 + P%)/100} × CP

SP = {(100 – L%)/100} × CP

Where P is Profit, L is loss, CP is cost price and SP is selling price.

Calculation:

SP2 = 70% of n

⇒ (70/100) × n

Loss = 19.5%

⇒ SP2 = {(100 – 19.5)/100} × CP

⇒ (70/100) × n = {(100 – 19.5)/100} × CP

⇒ 70n = 80.5CP

⇒ n = 1.15CP

⇒ n = (115/100) × CP

⇒ n = {(100 + 15)/100} × CP

n(original selling price) is 15% more than CP

I. If original selling price is Rs. 920, cost price is Rs. 800

CP = Rs. 800

n is 15% more than CP

Original selling price = (115/100) × 800

⇒ Original selling price = Rs. 920

⇒ I is correct

II. Original selling price is 12% more than cost price

n(original selling price) is 15% more than CP

⇒ II is incorrect

III. If cost price is Rs. 850, n will be Rs. 977.5

n = 115% of CP

⇒ (115/100) × 850

⇒ 977.5

⇒ III is correct.

I and III are correct.

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