A man sells an article at 5% above its cost price.If he had bought it at 5% less than what he paid for it and sold it for Rs 2 less , he would have gained 10%.Find the cost price of the article.
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•Cost price : The amount paid to purchase an article or the price at which an article is made is known as its cost price. The cost price is abbreviated as C.P.
•Selling price : The price at which an article is sold is known as its selling price. The selling price is abbreviated as S.P.
•Profit : If the selling price of an article is greater than the cost price , the difference between the selling price and the cost price is called profit.
SOLUTION :
Let the C.P of an article be ₹ x. Then S.P at a gain of 5%.
S.P = [(100 + gain%)/100] × C.P
S.P = [(100+5)/100] × x
S.P = 105x /100
If he had bought the article at 5% less , C.P = x - (5% of x ) = x - (5x/100)
C.P = x - 5x/100 = (100x - 5x)/100 = 95x /100
C.P = 95x/100
If the article sold for ₹ 2 less,then gain is 10%
S.P = 105x/100 -2 =(105x - 200)/100
S.P =(105x - 200)/100
Profit = 10% of C P = 10% of 95x/100
Profit = 10/100 × 95x/100 = 95x/1000
Profit = S.P - C.P
95x/1000 = (105x - 200)/100 - 95x/100
95x/1000 =[ (105x - 200 - 95x)/100]
95x/1000 =(105x - 95x - 200)/100
95x/1000 = (10x - 200)/100
(95x× 100) /1000 = (10x - 200)
95x/10 = (10x - 200)
95x/10 - 10x = -200
(95x -100x)/10 = -200
- 5x = - 2000
x = 2000/5
x = 400
Hence, C.P of an article is ₹ 400.
HOPE THIS WILL HELP YOU…..
•Selling price : The price at which an article is sold is known as its selling price. The selling price is abbreviated as S.P.
•Profit : If the selling price of an article is greater than the cost price , the difference between the selling price and the cost price is called profit.
SOLUTION :
Let the C.P of an article be ₹ x. Then S.P at a gain of 5%.
S.P = [(100 + gain%)/100] × C.P
S.P = [(100+5)/100] × x
S.P = 105x /100
If he had bought the article at 5% less , C.P = x - (5% of x ) = x - (5x/100)
C.P = x - 5x/100 = (100x - 5x)/100 = 95x /100
C.P = 95x/100
If the article sold for ₹ 2 less,then gain is 10%
S.P = 105x/100 -2 =(105x - 200)/100
S.P =(105x - 200)/100
Profit = 10% of C P = 10% of 95x/100
Profit = 10/100 × 95x/100 = 95x/1000
Profit = S.P - C.P
95x/1000 = (105x - 200)/100 - 95x/100
95x/1000 =[ (105x - 200 - 95x)/100]
95x/1000 =(105x - 95x - 200)/100
95x/1000 = (10x - 200)/100
(95x× 100) /1000 = (10x - 200)
95x/10 = (10x - 200)
95x/10 - 10x = -200
(95x -100x)/10 = -200
- 5x = - 2000
x = 2000/5
x = 400
Hence, C.P of an article is ₹ 400.
HOPE THIS WILL HELP YOU…..
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Heya !!
Here's your answer.. ⬇⬇
Let value of C.P be ( x )Rs.
Given :- gain % = 5%
S.P = ( 100 + gain% )/100 × C.P
S.P = ( 100 + 5 )/100 × x
S.P = 105/100 × x
S.P = 105x/100
S.P = 21x/20
Given :- Loss% = 5%
S.P = ( 100 - loss% P/100 × C.P
S.P = ( 100 - 5 )/100 × x
S.P = 95x/100
S.P = 19x/20
If sold it for 2 Rs. Less.
S.P = 21x/20 - 2
S.P = (21x - 40)/20
This case gain% = 10%
19x/20 × 110/100 = ( 21x - 40 )/20
209x/200 = ( 21x - 40 )/20
209x/200 = ( 21x - 40 )/20
( 209x/200 ) × 20 = 21x - 40
209x/10 = 21x - 40
209x = ( 21x - 40 ) × 10
209x = 210x - 400
210x - 209x = 400
x = 400
C.P ( x ) = 400 Rs.
Hope it helps..
Thanks (:
Here's your answer.. ⬇⬇
Let value of C.P be ( x )Rs.
Given :- gain % = 5%
S.P = ( 100 + gain% )/100 × C.P
S.P = ( 100 + 5 )/100 × x
S.P = 105/100 × x
S.P = 105x/100
S.P = 21x/20
Given :- Loss% = 5%
S.P = ( 100 - loss% P/100 × C.P
S.P = ( 100 - 5 )/100 × x
S.P = 95x/100
S.P = 19x/20
If sold it for 2 Rs. Less.
S.P = 21x/20 - 2
S.P = (21x - 40)/20
This case gain% = 10%
19x/20 × 110/100 = ( 21x - 40 )/20
209x/200 = ( 21x - 40 )/20
209x/200 = ( 21x - 40 )/20
( 209x/200 ) × 20 = 21x - 40
209x/10 = 21x - 40
209x = ( 21x - 40 ) × 10
209x = 210x - 400
210x - 209x = 400
x = 400
C.P ( x ) = 400 Rs.
Hope it helps..
Thanks (:
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