Assistance Required - Percentage Problem

[naveed_786110]

A factory produces an average of one defective unit after every 10 good units. The cost of producing one unit is Rs. 12. The defective unit also costs Rs. 12 but is sold as scrap for Rs. 2. The selling price of the good units if the manufacturer wants to earn a profit of 20% of total sales is:
a) Rs. 15.2
b) Rs. 16.2
c) Rs. 16.4
d) Rs. 16.3

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I tried to solve it by the following method. Please guide me.
If 11 units are made, Cost of first 10 units = 120, Cost of 11th item = 12-2=10. Total Cost of producing 11 units = 130

Profit = 20% of Total Sales
SP-CP = 20/100 x 11
SP-130 = 1/5 x 11
SP = 132.2 ( of 11 items)
SP= 12.018 (each unit)
But answers doesn't match.

 

[Ishuda]

There are a couple of things wrong which may basically be the way the problem is read and so I present a slight different example the Denis did. Lets just change the numbers to "A factory produces an average of one defective unit after every 20 good units. The cost of producing one unit is Rs. 15. The defective unit also costs Rs. 15 but is sold as scrap for Rs. 3.75 The manufacturer wants to earn a profit of 20% of total sales, what is the selling cost of the good units?"
Cost C: 21 units at 15 Rs.
C = 15 * 21 = 315
Total income I: You sell 20 units for x Rs. and 1 unit for 3.75 Rs.
I = 20 x + 3.75
but also income is cost plus (gross) profit, so
I = C + P
Profit P: 20% of total income
P = 0.2 I = 0.2 * (20 x + 3.75) = 4 x + 0.75

Put it together
I = 20 x + 3.75 = 315 + 4x + 0.75
16 x = 312
Selling cost x is given by
x = 19.5 Rs.

 

[naveed_786110]

There are a couple of things wrong which may basically be the way the problem is read and so I present a slight different example the Denis did. Lets just change the numbers to "A factory produces an average of one defective unit after every 20 good units. The cost of producing one unit is Rs. 15. The defective unit also costs Rs. 15 but is sold as scrap for Rs. 3.75 The manufacturer wants to earn a profit of 20% of total sales, what is the selling cost of the good units?"
Cost C: 21 units at 15 Rs.
C = 15 * 21 = 315
Total income I: You sell 20 units for x Rs. and 1 unit for 3.75 Rs.
I = 20 x + 3.75
but also income is cost plus (gross) profit, so
I = C + P
Profit P: 20% of total income
P = 0.2 I = 0.2 * (20 x + 3.75) = 4 x + 0.75

Put it together
I = 20 x + 3.75 = 315 + 4x + 0.75
16 x = 312
Selling cost x is given by
x = 19.5 Rs.

Great.....Really thankful to you for guidance.....I tried the question by same approach and got answer 16.3, which is the correct answer(I think)...... Why did you change numeric values?

 

[Ishuda]

... Why did you change numeric values?

The site is to help solve problems (whether homework or otherwise) and not necessarily to do problems. Thus, in many cases, as here, worked through examples are given to try to help teach a method rather than just solve a particular problem.