Question

Oranges can be packed in sets of 10 oranges in box type a or 25 oranges in box type



b. A carton comprising of 1000 oranges of type a and b is packed. How many different combinations are possible in the number of type a and type b boxes while organizing the oranges?

Answer 1

Box A can contain 10 oranges and Box B can contain 25 oranges so the equation is XA + YB=1000, we know the values for A&B so Equ becomes 10X + 25B=1000 => 2X + 5B=200, so fro the equation it is clear that the basic two values of X,Y are (0,40) & (100,0). Clearly if X increases by 5 then Y should decrease by 2 in order to maintain the constant value i.e 1000 oranges. so the different combinations will be (50,20) (55,18) (60,16) (65,14) (70,12) (75,10) (80,8) (85,6) (90,4) (95,2) (100,0) (45,22) (40,24) (35,26) (30,28) (25,30) (20,32) (15,34) (10,36) (5,38) (0,40 ) so there are 21 different combination by which we can arrange the oranges in the carton.