A 15% discount is allowed by a tradesman. How much above the cost price (in percentage) must he mark his goods so as to gain 19%?

We can establish the relationship between Cost Price (CP) and Marked Price (MP) using the standard formula:
CP
MP
​
=
100−Discount%
100+Profit%
​

Given data:

Discount%=15%

Profit%=19%

Substitute these values into the ratio equation:

CP
MP
​
=
100−15
100+19
​

CP
MP
​
=
85
119
​

Simplifying by dividing both numerator and denominator by 17:

CP
MP
​
=
5
7
​

The percentage markup above the cost price is:

Percentage Markup=
CP
MP−CP
​
×100
Percentage Markup=
5
7−5
​
×100=
5
2
​
×100=40%