How many total number of possible cases are there and which are those?

Question

Total cost of 1 kg apple, 1 kg grape and 2 kg banana is 210 Rupees.

If cost of fruits are in the order as given below
Cost of banana (1kg) =< Cost of grape (1kg) =< Cost of apple (1kg)
and all costs are multiple of 10 Rupee and minimum and maximum cost of any fruit per Kg is ranging from 30 Rupees to 90 Rupees.

How many total number of possible cases are there and which are those?

Answer 1

Making equation let A for Apple, B for Banana and G for Grape,

A + G + 2B = 210

ans condition is B =< G =< A

range is [ 30, 90 ]

So total possible solutions which staisfies the condition and equation both will be 6

(1) A = 90 , B = 30 , G = 60
(2) A = 80 , B = 30 , G = 70
(3) A = 90 , B = 40 , G = 40
(4) A = 80 , B = 40 , G = 50
(5) A = 70 , B = 40 , G = 60
(6) A = 60 , B = 50 , G = 50