Question

A Fruit seller buys a certain dozen of apples at Rs.324. he sold a 1/3rd of apples at 33(1/3) % profit on each apple and sold 25% of the remaining apples at 66(2/3)% less profit on each apple than in previous sale. He sold the rest of the apples such that he gets Rs. 2(13/30) profit on each apple and 40% profit overall sale. Find the CP of one dozen of apples.

Answer 1

Answer:

Cost Price of one dozen of apples = Rs 54

Step-by-step explanation:

Let say fruit seller  buy    A dozen of apples at rs 324

Cost Price of one dozen = 324/A

One third of apple in dozens =   A/3

Sold at profit of 100/3%

Selling Price per dozen  = (324/A)(1 + 1/3)   = 432/A

Selling price for A/3 dozen =  (432/A)(A/3)  = 144  Rs

Remaining apples in dozens = A - A/3 = 2A/3

25% of remaining apples = (25/100)(2A/3)  = A/6

Profit in earlier sale = 100/3%

Profit in this sale = (200/3)% less Means  (100/3)% of earlier sale

=> Profit in this sale =  100/9 %

Selling Price in this sale per dozen =  324/A( 1 + 1/9)  = 360/A

Selling price for A/6 dozen =  (360/A)(A/6)  = 60  Rs

Rest of the apples in dozen = A - A/3  - A/6  =  (A/6)(6 - 2 - 1) = A/2

Profit on each apple  = 73/30

Profit on one dozen apple = 12 * 73/30  = 146/5 Rs

Selling price per dozen = (324/A + 146/5)  Rs

Selling Price of A/2 Dozens = (A/2)(324/A + 146/5)   = 162  + 14.6A  

Total selling Price = 144 + 60 + 162 + 14.6A =  366 + 14.6A

Over all profit = 40% overall sale

Selling Price = 324 ( 1 + 40/100) = 324 * 1.4 = 453.6 Rs

366 + 14.6A  = 453.6

=> 14.6A = 87.6

=> A = 6

Cost Price of one dozen = 324/A  =  324/6

= 54

Cost Price of one dozen of apples = Rs 54