Correct Answer - Option 2 : II and III
Given:
Profit on 20 buffaloes = 12.5%
Total buffaloes sold = 35
Total profit = 20%
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 buffalo is CP
Profit on 20 buffaloes = 12.5% of CP of 20 buffaloes
⇒ (12.5/100) × 20 × CP
Let the profit on 15 buffaloes is P%.
⇒ Profit on 15 buffaloes = (P/100) × 15 × CP
Total Profit = 20% of CP of 35 buffaloes
⇒ Profit on 20 buffaloes + Profit on 15 buffaloes = (20/100) × 35 × CP
⇒ (12.5/100) × 20 × CP + (P/100) × 15 × CP = 7CP
⇒ CP(2.5 + 3P/20) = 7CP
⇒ 2.5 + 3P/20 = 7
⇒ 3P/20 = 4.5
⇒ P = 30
I. In the latter transaction, he gains 140% more than the first transaction.
More% = [(30 – 12.5)/12.5] × 100
⇒ (17.5/12.5) × 100
⇒ 140%
⇒ Only I is incorrect.
∴ I and III are correct
Short Trick:
Profit% 12.5% 30%
Overall 20
Buffaloes 10 ∶ 7.5