# A shopkeeper buys apple @Rs. A per kg and orange @Rs. O per kg. He sells apples at a profit of 13% and oranges at a profit of 8%. His total gain is Rs

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A shopkeeper buys apple @Rs. A per kg and orange @Rs. O per kg. He sells apples at a profit of 13% and oranges at a profit of 8%. His total gain is Rs. 48.5. A is 50 more than O. Which of the following is/are correct?

A. A + O = 500

B. Average price of orange and apple is Rs. 225

C. A × O ÷ 100 = 500

D. A/O = 12.5

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

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Correct Answer - Option 3 : B and C

Given:

CP of orange = O per kg

CP of apple = A per kg

A = O + 50

Profit on orange = 8%

Profit on apple = 13%

Total gain = Rs. 48.5

Formula Used:

Profit = SP – CP

Profit% = (Profit /CP) × 100

SP = {(100 + P%)/100} × CP

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

Calculation:

Profit on orange = (8/100) × O

Profit on apple = (13/100) × A

Overall gain = Rs. 48.5

Profit on orange + Profit on apple = 48.5

⇒ (8/100) × O + (13/100) × A = 48.5

Putting A = O + 50

⇒ (8/100) × O + (13/100) × (O + 50) = 48.5

⇒ 8O + 13O + 650 = 4850

⇒ 21O = 4200

O = 200

⇒ A = 200 + 50

A = 250

A. A + O = 500

250 + 200 = 450

⇒ A is incorrect

B. Average price of orange and apple is Rs. 225

(200 + 250)/2 = 450/2

⇒ 225

⇒ B is correct

C. A × O ÷ 100 = 500

250 × 200 ÷ 100 = 250 × 2

⇒ 500

⇒ C is correct

D. A/O = 12.5

250/200 = 1.25

⇒ D is incorrect

∴ B and C are correct.