The selling price of a product is fixed to ensure a 40% profit. If the product had cost 40% less and had been sold for 5 rupees less, the resulting profit would have been 50%. We need to find the original selling price.
1
Let the original cost price be
CP.
2
The original selling price
SP is given by:
SP=1.4×CP
3
The new cost price after a 40% reduction is:
New CP=0.6×CP
4
The new selling price after a 5 rupee reduction is:
New SP=SP−5=1.4×CP−5
5
The profit percentage in the second scenario is 50%, so:
(New CPNew SP−New CP)×100=50
6
Substituting the values:
(0.6×CP1.4×CP−5−0.6×CP)×100=50
7
Simplifying the numerator:
(0.6×CP0.8×CP−5)×100=50
8
Converting to an equation:
0.6×CP0.8×CP−5=0.5 0.8×CP−5=0.3×CP 0.5×CP=5⟹CP=10
11
The original selling price is:
\[ SP = 1.4 × 10 = 14
