Question

Aniket sells 20 buffaloes at a gain of 12.5% and 15 more at a certain gain percent. If he gains 20% on the whole which of the following is correct?

I. In selling 15 buffaloes, he gains 25%

II. In selling 15 buffaloes, he gains 30%

III. In the latter transaction, he gains 140% more than the first transaction.

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

Answer 1

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