If selling price of 10 kg sugar is same as cost price of 11 kg of sugar.find the gain percent.
20%
25%
10%
None of these
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We take the cost of 1kg of sugar = Rs. x
So the price =100x.
The shopkeeper sold 20 kg of sugar at 20% profit.
Then the profit on 100 kg of sugar at 12%= 100x×
100
12
=12x .......(i)
Let the sugar be divided into p kg and (100−p) kg.
So the price of p kg =px.
Then the profit on p kg at 10%= px×
100
10
=
10
px
..........(ii).
Again the price of 100−pkg=(100−p)x.
Then the profit on (100−p) kg at 20%= (100−p)x×
100
20
=
10
(200−2p)x
..........(iii).
Then, adding (ii) & (iii), the total profit =
10
px
+
10
(200−2p)
=
10
x(200−p)
∴
10
x(200−p)
=12x ....(comparing with (i))
⇒200−p=120
⇒100−p=(100−80) kg =20 kg
So, the shopkeeper sold 20 kg of rice at 20% profit.
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