Question

The cost of manufacture of an article is made up of four components a, b, c and d which have a ratio of 3 : 4 : 5 : 6 respectively. if there are respective changes in the cost of + 10%,-20%,-30% and + 40%, then what would be the percentage change in the cost.

Answer 1

Given the ratio of cost of manufacture as 3:4:5:6

Lets assume values as 30 , 40, 50 & 60 (3:4:5:6)

Now respective change in costs are given as 10% increase , 20% decrease, 30% decrease, 40% increase.
10% increase on A== 30*110/100 = 33
20% decrease on B== 40*80/100 = 32
30% decrease on C== 50*70/100 = 35
40% increase on D==60*140/100 = 84
Initial cost(total) = 30+40+50+60 = 180
Final cost = 33+32+35+84 = 184
Change in cost = 184-180 = 4 Rs.
% change in cost = 4/180 * 100 = 2.22% increase

Answer 2

So there will be an increment in the cost and the percentage of increment is 2.22%.

Given:

Given the ratios of articles are 3:4:5:6 and there is an increment of 10%, decrement of 20%, decrement of 30%, and increment of 40%.

To Find:

The percentage of change in cost

Solution:

Let's assume values of those ratios as, 30, 40, 50, and 60. And given that there is an Increment of 10%, Decrement of 20%, Decrement of 30%, And increment of 40%.

If we consider the total cost of the article as 100%, then,

For 10% increment => 100% + 10% = 110%

For 20% decrement=> 100% - 20% = 80%

For 30% decrement=> 100% - 30% = 70%

For 40% increment=> 100% + 40% = 140%

So the article 'A' with percentage of 110% => 30×110% = 30×110/100=33

So the article 'B' with percentage of 80% => 40×80% = 40×80/100=32

So the article 'C' with percentage of 70% => 50×70% = 50×70/100=35

So the article 'D' with percentage of 140% =>60×140% = 60×140/100=84

∴ So the Initial cost = 30+40+50+60 = 180

∴ Final cost = 33+32+35+84 = 184

Change in cost = Final cost - Initial cost,

=> 184-180 = 4Rs.

∴ Percentage of change in the cost =4×180 = 4×180/100 =

2.22% increment.

There will be an increase in the total change and the percentage of increment is 2.22%.