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The price of raw materials has gone up by 15%, labour cost has also increased from 25% of the cost of raw material to 30% of the cost of raw material. By how much percentage should there be a reduction in the usage of raw materials so as to keep the cost the same?

  • a)
    16%

  • b)
    15%

  • c)
    28%

  • d)
    25%

  • e)
    17%

Correct answer is option 'E'. Can you explain this answer?
Verified Answer
The price of raw materials has gone up by 15%, labour cost has also in...
Let the number = 1

Then, ideally he should have multiplied 1 by 5/3. 

Hence the correct result was 1 x (5/3) = (5/3)

By mistake, he multiplied 1 by 3/5. 

Hence the result with the error = 1 x (3/5) = (3/5)

This question is part of UPSC exam. View all Quant courses
Most Upvoted Answer
The price of raw materials has gone up by 15%, labour cost has also in...
If percentage change comes 16.38, why are we choosing 17 insted of 16, for the answer??
Community Answer
The price of raw materials has gone up by 15%, labour cost has also in...
Given:
- Increase in price of raw material = 15%
- Increase in labor cost = 5% (from 25% to 30% of the cost of raw material)

To keep the cost the same, we need to reduce the usage of raw material.
Let's assume the initial cost of raw material = 100 units.
Therefore, the initial cost of labor = 25 units (25% of 100 units).

After the increase in price of raw material by 15%, the new cost of raw material = 115 units.
The new cost of labor = 30% of 115 units = 34.5 units.

Total cost = 100 + 25 = 125 units (initially)
Total cost = 115 + 34.5 = 149.5 units (after increase)

To keep the cost the same, we need to reduce the total cost by 24.5 units (149.5 - 125).

Let's assume the percentage reduction in usage of raw material = x%
Therefore, the new cost of raw material = 100 - (x% of 100) = 100 - x units.
The new cost of labor = 30% of (100 - x) units.

Total cost = (100 - x) + 30% of (100 - x) = 125 - 24.5
(30% of (100 - x) = 24.5)

Solving for x, we get x = 16%.

Therefore, the percentage reduction in usage of raw material should be 16% to keep the cost the same.
Hence, option E is the correct answer.
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The price of raw materials has gone up by 15%, labour cost has also increased from 25% of the cost of raw material to 30% of the cost of raw material. By how much percentage should there be a reduction in the usage of raw materials so as to keep the cost the same?a)16%b)15%c)28%d)25%e)17%Correct answer is option 'E'. Can you explain this answer?
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