If the market price of a bedsheet is 24% above the cost price and a discount of 15% is declared on it, then find the gain percentage.
- A5.30%
- B5.10%
- C5.20%
- D5.40%
Solution & Step-by-step Explanation
Let the Cost Price (CP) of the bedsheet be 100.
The Marked Price (MP) is 24% above the CP:
MP=100+24=124
A discount of 15% is given on the MP:
Discount=15% of 124=
100
15
×124=18.6
The Selling Price (SP) is:
SP=MP−Discount=124−18.6=105.4
Since CP=100 and SP=105.4:
Gain %=SP−CP=105.4−100=5.4%
Alternative Method (Successive Percentage Formula):
Net Percentage Change=a+b+
100
ab
Where a=+24% (markup) and b=−15% (discount):
Gain %=24−15+
100
24×(−15)
Gain %=9−
100
360
=9−3.6=5.4%
The Marked Price (MP) is 24% above the CP:
MP=100+24=124
A discount of 15% is given on the MP:
Discount=15% of 124=
100
15
×124=18.6
The Selling Price (SP) is:
SP=MP−Discount=124−18.6=105.4
Since CP=100 and SP=105.4:
Gain %=SP−CP=105.4−100=5.4%
Alternative Method (Successive Percentage Formula):
Net Percentage Change=a+b+
100
ab
Where a=+24% (markup) and b=−15% (discount):
Gain %=24−15+
100
24×(−15)
Gain %=9−
100
360
=9−3.6=5.4%