3. A shopkeeper bought an article and sold it at a gain of 10%. If he had bought it at 20%
less and sold it for Rs 30 more, he would have made a profit of 45%. Find the cost price
of the article.
Answers
Answer:
Rs. 2000
Step-by-step explanation:
Let original CP of the article was X.
First Case:
Gain = 10%
SP = [100 + gain%/100] * CP
SP = [(100+ 10)/100]X = 110X/100 = 11X/10
Second Case:
If CP is 20% less
New CP = (100 - 20/100)X = 80X/100 = 4X/5.
He would have gained 40%
so, (11X/10 + 30) - 4X/5 = 40% of 4X/5
=> 11X/10 - 4X/5 + 40 = 40/100 * 4X/5
=> 3X/10 + 40 = 8X/25
=> 8X/25 - 3X/10 = 40
=> 16X - 15X/50 = 40
=> X = 40*50 = Rs. 2000
Answer
Let the C.P be x
Gain= 10%
If C.P is ₹100,then S.P =₹110
If C.P is ₹x , then S.P=₹110/100x
Now
S.P= ₹110/100x
New C.P = ₹(x — 20% of C.P)= x- 20/100x) = ₹80/100x
Gain 45%
If C.P = 100,then S.P = ₹145
If C.P = ₹80/100x , then S.P =₹145/100X80/100x =₹116/100x
As per given condition
New S.P is ₹30 more than original S.P
116/100x — 110/100x =30
6/100x=30
x= 30/6 X 100 =500
Hence , cost price of article is ₹500