A machine produces a certain item at a rate of 200units per hour.

Question

A machine produces a certain item at a rate of 200units 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

a.300
b.302
c.308
d.306

a.300
b.302
c.308
d.306

Kinshook · Answer

Given: 
1. A machine produces a certain item at a rate of 200units per hour. 
2. The cost of each item produced is 6 and S.P is 12 None of the items are defective.

Asked: 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

For 300 units/hour production rate; 
Rate of production is increased by 50% ; 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

robert2345 
None of the answer choices match the correct answer. Please check the question.

CareerGeek · Answer

% increase in rate of production, y% = (300 - 200)/200*100 = 100/200*100 = 50%

Number of defective = (4 + 0.05y) = (4 + 0.05*50) = 6.5% = 6.5/100*300 = 19.5
—> Number of units that are non-defective = 300 - 19.5 = 280.5

Increase in cost of production = y/2% = 25%
—> New cost price = 6(1 + 25/100) = 7.5

Profit = SP - CP
= 280.5*12 - 300*7.5 = 3366 - 2250 = 1116

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globaldesi · Answer

% 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 prods 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

No matching answer

rajatchopra1994 · Answer

% increased by 50% ; therefore, y = 50
Number of defective = (4 + 0.05y) = (4 + 0.05*50) = 6.5% 
= 300*6.5% = 19.5 = 20 (aprox)

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

Kinshook · Answer

Dillesh4096 
Number of defective units must be in integers.

bumpbot · Answer

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A machine produces a certain item at a rate of 200units per hour.

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