(xiii) If the profit of a thing is p% on the selling price, then what is the rate of profit on the cost price?
(a) \(\frac{100p}{100-p} %\)
(b) \(\frac{100-p}{100p} %\)
(c) \((1+\frac{p}{100}) %\)
(d) none of these
Answer (1)
To find the rate of profit on the cost price when the profit is given as a percentage of the selling price (p%), we need to understand the relationship between selling price, cost price, and profit.
Definitions :
Let SP be the selling price.
Let CP be the cost price.
Let Profit be the monetary amount of profit earned.
Given Relationship :
We know that the profit as a percentage of the selling price is given by: Profit = ( 100 p ) × SP
Relation Between SP and CP :
The selling price is always the cost price plus profit. Therefore, SP = CP + Profit
Substitute Profit from SP into CP :
Substitute the equation for Profit from point 2 into the equation for SP: SP = CP + ( 100 p ) ⋅ SP
Rearrange to solve for CP: CP = SP ( 1 − 100 p )
Finding Rate of Profit on CP :
The profit as a percentage of the cost price is calculated as: Rate of profit on CP = ( CP Profit ) × 100%
Substitute for Profit and CP: Rate of profit on CP = ( SP ( 1 − 100 p ) ( 100 p ) ⋅ SP ) × 100% = ( 1 − 100 p p ) × 100%
Simplify the expression: = 100 − p 100 p %
Thus, the correct option is (a) 100 − p 100 p % .
