​A man purchased 50 dozen bananas for a certain amount. He could not sell five dozen of those bananas as they were spoiled. He sold two-thirds of the good bananas at a profit of 20% per dozen and sold the remaining good bananas at a profit of 5% per dozen. What was his loss or gain percentage in the whole transaction?

Correct option is A

​Given :

Total bananas purchased: 50 dozen bananas.

Spoiled bananas: 5 dozen bananas spoiled, so only 45 dozen are good.

Formula Used:​

Gain % = $$\frac{\text{Gain}}{\text{Cost Price}}\times 100$$​​

Solution :

Selling profits:

Two-thirds of the good bananas = $$\frac{2}{3} \times 45$$ = 30 dozen.( 20% profit per dozen)

One-third of the good bananas = $$\frac{1}{3} \times 45$$​ = 15 dozen( 5% profit per dozen)

Let the cost price of 1 dozen bananas be C.

Total cost of 50 dozen = 50C

Selling price of good bananas:

For 30 dozen bananas sold at 20% profit: 30 × C × 1.20 = 36C.

For 15 dozen bananas sold at 5% profit: 15 × C × 1.05 = 15.75C

Total selling price of the good bananas= 36C + 15.75C = 51.75C

Total gain or loss:

The total selling price = 51.75C

Total cost price = 50C

Gain= 51.75C−50C =1.75C.

Gain percentage = $$\frac{1.75C}{50C} \times 100 = 3.5\%$$​​

Thus, the man has a 3.5% gain.