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The cost of manufacturing of an article depends upon four components P, Q, R, S. Cost ratio of P, Q, R, S is 4:5:6:7 respectively. If there is a respective change of 30%, -20%, -8.33% and +20% in the cost of four components then by how much percent it would affect the manufacturing cost of the article. 
  • a)
    10% 
  • b)
    20% 
  • c)
    5% 
  • d)
    15% 
Correct answer is option 'C'. Can you explain this answer?
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Solution:

Given, the cost ratio of P, Q, R, S is 4:5:6:7 respectively.

Let the cost of P, Q, R, S be 4x, 5x, 6x, 7x respectively.

Now, the respective change in the cost of four components are:

- 30% increase in P, so the new cost of P = 4x + (30/100) * 4x = 5.2x
- 20% decrease in Q, so the new cost of Q = 5x - (20/100) * 5x = 4x
- 8.33% decrease in R, so the new cost of R = 6x - (8.33/100) * 6x = 5.5x (approx.)
- 20% increase in S, so the new cost of S = 7x + (20/100) * 7x = 8.4x

Therefore, the new cost ratio of P, Q, R, S is 5.2:4:5.5:8.4

The new total cost of manufacturing = 5.2x + 4x + 5.5x + 8.4x = 23.1x

The initial total cost of manufacturing = 4x + 5x + 6x + 7x = 22x

% change in manufacturing cost = [(New cost - Initial cost)/Initial cost] * 100

= [(23.1x - 22x)/22x] * 100

= 4.54%

Therefore, the manufacturing cost of the article would be affected by 5% (approx.)

Hence, option (c) is the correct answer.
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The cost of manufacturing of an article depends upon four components P, Q, R, S. Cost ratio of P, Q, R, S is 4:5:6:7 respectively. If there is a respective change of 30%, -20%, -8.33% and +20% in the cost of four components then by how much percent it would affect the manufacturing cost of the article.a)10%b)20%c)5%d)15%Correct answer is option 'C'. Can you explain this answer?
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