Wayne has a weighing machine that shows 20% more weight than the actual. At what percent more than the cost price should he sell so as to make a profit of 35%?
Solution
Correct Answer: Option B
The weighing machine shows a 20% increased weight.
Suppose Wayne sells weight N units of a commodity for which cost price per unit is T.
If N units weight is measured, the weight machine will show = [N + N × (20/100)] units = 1.2N units
Because of this fault, Wayne will sell N units, but will take price of 1.2N units.
Cost price for Wayne = N units × Rs. T per unit = Rs. NT
Suppose Wayne sells at P percent more than cost price.
We know, Selling Price = Cost Price × (1 + (Profit Percentage)/100)
Selling Price of one unit \(= T \times \;\left( {1 + \;\frac{P}{{100}}} \right)\)
Selling Price of 1.2N units \(= 1.2NT \times \;\left( {1 + \;\frac{P}{{100}}} \right)\)
For profit to be 35%,
Selling Price of N units \(= Cost\;Price\;of\;N\;units \times \;\left( {1 + \;\frac{{35}}{{100}}} \right)\)
\(\begin{array}{l} 1.2NT \times \;\left( {1 + \;\frac{P}{{100}}} \right) = 1.35\;NT\\ \left( {1 + \;\frac{P}{{100}}} \right) = \frac{{1.35}}{{1.2}} \end{array}\)
P = 100 × (1.125-1)= 12.5
∴ To make a profit of 35%, commodities should be sold at 12.5% more than cost price.
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