The different between the number of units of product A produced by company X and 40% of the number of units of products D produced by company Y is k. The value k lies between.

The following points are given in the question.

i)The total units of all these products produced by X and Y together are 5500, and company Y produces 20% more units than company X.

Let x be the number of products from company X. Then the number of products from company Y will be x+$$\frac{20}{100}$$ = 1.2x

x+1.2x=2.2x=5500

$$\Rightarrow$$ x =2500

The number of products from company x is 2500, and that from y is 1.2*2500=3000

ii) Out of the total units of the products produced by company Y, 12% are of product B, and company X produces 30% more units of B than Y.

Given that 12% of Y products are B.

12% of 3000 = 360. Company Y produces 360 products of type B.

company X produces 30% more units of B than Y.

Company X produces 468 products of type B.

iii) The ratio of the units of product A produced by companies X and Y is 5: 6, and the total number of units of A is 990.

Let's say the constant proportionality of the given ratio is k. 5k+6k = 11k = 990.

$$\Rightarrow$$ k = 90

Company X produces 450 products of type A, and Company Y produces 540 products of type A.

iv) The number of units of product D produced by company X is 650, and company Y produces 40% more of it.

The number of units of product D produced by company X is 650.

Company Y produces 40% more than company X. That will be 910.

v) company X produces 550 units of C, and Company Y produces 55 more.

Company X produces 550 units of C. And Company Y produces 605(55 more).

vi) The units of the products left with companies X and Y are of product E.

The product left for company X is 382, and that for company Y is 585.

The number of units of product A produced by company X is 450.

40% of the number of units of products D produced by company Y is $$\frac{40}{100}$$*910 = 364

450 - 364 = 86

So, k is 86.