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