how much percent above the cost price should a shopkeeper mark his goods so that after allowing a discount of 20percent on the marked price, he gains 12percent
Answers
let the CP be Rs. 100 and MP be Rs. x
gain % after discount = 12%
gain = 12% of 100 = Rs. 12
⇒ SP of the article = CP + Gain
= Rs. (100 + 12) = Rs. 112
Discount % = 20%
Discount = 20% of Marked Price
= Rs.20/100 * x
= Rs. 20x/100
= Rs. x/5
as da question says
marked Price - discount = SP
=> x - x/5 = 112
=> (5x - x)/5 = 112
=> 4x/5 = 112
=> x = 112 * 5/4 = Rs. 140
marked Price = Rs. 140
amount marked above the CP = MP - CP
= Rs. (140 - 100)
= Rs. 40
∴ % amount marked above the CP
= Amount increased/CP * 100
= 40/100 * 100
=40%
Hope it helps
- Marked price of goods must be 40% above cost price in order to gain 12% after giving 20% discount .
Given :-
- Discount = 20%
- Gain = 12%
To Find :-
- How much percent above the cost price is marked price ?
Formula used :-
- Selling price (SP) = {CP × (100 + gain%)}/100
- Marked price (MP) = (SP × 100) / (100 - Discount %)
Solution :-
Let us assume that, the cost price of the goods is equal to Rs. 100x .
So,
→ CP of goods = Rs. 100x
→ Gain = 12%
then,
→ SP of goods = {CP × (100 + gain%)}/100
→ SP = {100x × (100 + 12)}/100
→ SP = (100x × 112)/100
→ SP = Rs. 112x .
Now,
→ SP of goods = Rs. 112x
→ Discount = 20%
→ MP of goods = (SP × 100) / (100 - Discount %)
→ MP = (112x × 100) / (100 - 20)
→ MP = (112x × 100) / 80
→ MP = Rs. 140x
therefore, marked price above cost price :-
→ MP - CP = 140x - 100x = Rs. 40x
hence,
→ Required % = (40x × 100) / 100x
→ Required % = 40% (Ans.)
∴ Marked price of goods must be 40% above cost price .
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