A machine produces a certain item at a rate of 200 units per hour GMAT Problem Solving

Question: A machine produces a certain item at a rate of 200 units per hour. The cost of each item produced is 6 and S.P is 12 None of the items are defective. If the rate of production is increased by y%, the no: of defective units become (4+0.05y)% and the cost of production of each item increases by (y/2)%. Find the profit ( per hour) if the machine production is 300 units per hour

  • 300
  • 302
  • 308
  • 306

Approach Solution (1)

As percentage is increased by 50%
Therefore, y = 50
Number of defective = (4 + 0.05y)% = (4 + 0.05*50)% = 6.5%
= 300*6.5% = 19.5 = 20 (approximately)

As cost of production increases by 25%
Cost of each item produced = 7.5

Profit per hour = SP - CP
= 280 * 12 - 300 * 7.5
= 3360 - 2250
= 1110

Correct option: No option matched

Approach Solution (2)

For 300 units/hour production rate;
Rate of production is increased by 50%
Thus, y = 50

Number of defective units = (4 + .05*50)% = 6.5% = 300*6.5% = 19.5 ~ 20 since number of defective units must be an integer
Cost of production increases by 25%
Cost of each item produced = 7.5
Profit per hour = (300 - 20) * 12 - 300 * 7.5 = 1350 - 240 = 1110

Correct option: No option matched

Approach Solution (3)

% increase in production = (300 - 200) / (200 * 100) = 50%
Thus y = 50
Put value of y back in all given scenarios

Increase in defects = (4 + .05*y)% = (4 + .05*50)% = 6.5% thus defects in 300 prods = 6.5 * 3 = 19.5 ~ 20
Thus, selling price will be 300 - 20 = 280
or S.P. = 280 * 12 = 3360

Product cost increase per item = 6 *(1 + y/2%) = 6*125 / 100 = 7.5
C.P of 300 items = 300 * 7.5 = 2250
Hence profit = 3360 - 2250 = 1110

Correct option: No option matched

“A machine produces a certain item at a rate of 200 units per hour. The cost of each item produced is 6 and S.P is 12 None of the items are defective. If the rate of production is increased by y%, the no: of defective units become (4+0.05y)% and the cost of production of each item increases by (y/2)%. Find the profit ( per hour) if the machine production is 300 units per hour”- is a topic of the GMAT  Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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