Given:
A person sells an article X at a profit of 12%. Had the cost price been 8% less and the selling price Rs. 14 less, his profit would have been 14%.
Formula Used:
Profit% = Profit/Cost Price × 100%
Loss% = loss/cost price × 100%
Selling price = CP × (100 + profit%)/100 or CP (100 - loss%)/100
Calculation:
Let cost price of article X = CP
Selling price (SP) = CP(100 + Profit%)/100
⇒ CP(100 + 12)/100 = CP × 112/100 = 28/25 CP
If CP becomes 8% less and SP Rs 14 less then, profit becomes 14% less,
New cP = CP × 92/100 = 23/25CP
New SP = (100 + new profit%) of new CP
⇒ (100 + 14%) of 23/25 CP
⇒ 114/100 × 23/25 CP
⇒ 57/50 × 23/25 CP = 1311/1250 CP
According to question,
New SP is Rs 14 less than initial SP
⇒ Initial SP - New SP = 14
⇒ 28/25 CP - 1311/1250 CP = 14
⇒ CP (28 × 50 - 1311)/1250 = 14
CP (1400 - 1311)/1250 = 14
CP(80/1250) = 14
CP = 14 × 1250/89 = 17500/89 = 196.6292 ≈ 196.63