Prachi sells 28 articles at a gain of 35% and 12 more at a certain gain percent. If he gains 29% on the whole, which of the following is NOT correct? I. In latter transaction profit on 12 articles is 12% II In the latter transaction, If the profit on 12 articles is P% then P% of 40 is 6.

Prachi sells 28 articles at a gain of 35% and 12 more at a certain gain percent. If he gains 29% on the whole, which of the following is NOT correct? I. In latter transaction profit on 12 articles is 12% II In the latter transaction, If the profit on 12 articles is P% then P% of 40 is 6. Correct Answer <span style=" line-height: 115%; background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;">Only II </span>

Given:

Profit on 28 articles = 35%

Total articles sold = 40

Total profit = 29%

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:

Let the cost price of one article is CP

Profit on 28 articles = 35% of CP of 28 articles

⇒ (35/100) × 28 × CP

Let the profit on 12 articles is P%.

⇒ Profit on 12 articles = (P/100) × 12 × CP

Total Profit = 29% of CP of 40 articles

⇒ Profit on 28 articles + Profit on 12 articles = (29/100) × 40 × CP

⇒ (35/100) × 28 × CP + (P/100) × 12 × CP = (29/100) × 40 × CP

⇒ 35 × 28 + P × 12 = 29 × 40

⇒ 4(245 + 3P) = 29 × 40

⇒ 245 + 3P = 290

⇒ 3P = 45

⇒ P = 15

I. In latter transaction profit on 12 articles is 12%

P% = 15%

⇒ I is incorrect

II In the latter transaction, If profit on 12 articles is P% then P% of 40 is 6.

P% of 40 = 15% of 40

⇒ (15/100) × 40

⇒ 6

∴ Only II is correct

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