Question

If the cost of bananas is increased by Rs. 10 per dozen, one can get 3 dozen less for Rs.600. Find the original cost of one dozen of bananas

Answer 1

Let x be the original cost of 1 dozen bananas , for Rs. 600 we  gets y dozens.  

xy =600 .................... {1}

$y=\frac{600}{x}$ 

By increasing the cost of 1 dozen of bananas by Rs. 10 we get 3 dozen less bananas

(x +10)(y - 3)=600  ..........................{2}

Substituting the y value in (2), we get 

$(x+10)(\frac{600}{x}-3)=600$ 

$(x+10)(\frac{(600-3x)}{x})=600$

$6000-30x-3x^2=0$ 

$3(x^2+10x-2000)=0$ 

$(x^2+10x-2000)=0$ 

(x+50)(x-40)=0

x=-50 or 40

Since cost of bananas cannot be negative, x = 40. So, the original cost of one dozen of bananas is Rs.40