An article is sold by a manufacturer for p percent more than what it costs to produce. Determine the percentage profit if he offers the buyer a discount of q%. [Answer Limit: 125 words] [UKPSC 2012]
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An article is sold by a manufacturer for p percent more than what it costs to produce. Determine the percentage profit if he offers the buyer a discount of q%. [Answer Limit: 125 words] [UKPSC 2012]
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Let the cost price (CP) of the article be ₹100.
The selling price (SP) at
𝑝
%
p% more than the cost price is:
𝑆
𝑃
=
100
+
𝑝
100
×
100
=
100
+
𝑝
=
(
100
+
𝑝
)
rupees
SP=100+
100
p
×100=100+p=(100+p) rupees
If the manufacturer gives a discount of
𝑞
%
q%, the discount amount is:
Discount
=
𝑞
100
×
(
100
+
𝑝
)
Discount=
100
q
×(100+p)
Thus, the actual selling price after discount is:
Actual SP
=
(
100
+
𝑝
)
−
𝑞
100
×
(
100
+
𝑝
)
=
(
100
+
𝑝
)
(
1
−
𝑞
100
)
=
(
100
+
𝑝
)
(
100
−
𝑞
100
)
Actual SP=(100+p)−
100
q
×(100+p)=(100+p)(1−
100
q
)=(100+p)(
100
100−q
)
The profit is calculated as:
Profit
=
Actual SP
−
𝐶
𝑃
=
(
100
+
𝑝
)
(
100
−
𝑞
100
)
−
100
Profit=Actual SP−CP=(100+p)(
100
100−q
)−100
The profit percentage is:
Profit Percentage
=
Profit
𝐶
𝑃
×
100
=
(
100
+
𝑝
)
(
100
−
𝑞
100
)
−
100
100
×
100
Profit Percentage=
CP
Profit
×100=
100
(100+p)(
100
100−q
)−100
×100
This simplifies to:
Profit Percentage
=
(
100
−
𝑞
)
+
𝑝
(
100
−
𝑞
)
100
−
100
=
𝑝
(
100
−
𝑞
)
100
−
𝑞
Profit Percentage=(100−q)+
100
p(100−q)
−100=
100
p(100−q)
−q
Thus, the profit percentage is:
Profit Percentage
=
𝑝
(
100
−
𝑞
)
100
−
𝑞
Profit Percentage=
100
p(100−q)
−q