Question

the cost to manufacture an article is made up of four components  A,B,C and D, which are used in the ratio of 3:4:5:6,respectively .if the price of these components changes as +10%,-20%,-30%,+40% respectively ,what would be the percentage change in the cost of the arcticle

Answer 1

Amounts of components used in making the article,  let us say, are    3x , 4x, 5x and 6x for A, B, C and D respectively. 
Previous prices of the components , let us say:  Rs a / unit material of A, Rs b / unit material of B , Rs c / unit of C and Rs d / unit of D.
Previous cost of manufacturing the article:  P =  x (3 a + 4b + 5 c + 6d)
New prices of the components : Rs a * 110 /100 for A ,  Rs 80 b /100 for B,
                                     Rs 70 c/ 100 for C  and Rs 140 d / 100 for D.
New cost of manufacturing = Q =  x ( 3a 1.1 + 4 b *0.8 + 5 c * 0.7 + 6 d * 1.4)
% change in cost = (Q - P) * 100 / P = 
               100 * (0.1 a - 0.2 b - 0.3 c + 0.4 d) /(3a+4b+5c+6d)
             = 10 (a - 2b - 3c + 4d) / (3a+4b+5c+6d)
You need to know the previous costs of the components to find the value of percentage change in the cost of the article.