An article is sold at 10% profit. If its cost price increased by 20rs and the selling price is increased by 10rs, the profit would be 10/9 %. Find the original cost price.
S-c = c/10
1 1/9 % = 10/9% = 10/900= 1/90
S+10 - ( c+20) = (c+20) /90
S+10 - c-20 = (c+20) /90
S - c +10 -20 = (c+20) /90
S - c -10 = (c+20) /90
S - c =( (c+20) /90 )
S - c =10 + ( (c+20) /90)
S - c =10 + ( (c+20) /90)
c/10 = 10 + ( (c+20) /90)
(c/10 ) - ( (c+20) /90) =10
(9c/90 ) - ( (c+20) /90) =10
(9c-c-20) /90) =10
(8c-20) /90) =10
(8c-20) /90) =10
8c -20 =900
8c = 920
C = 115
Let initial cost price (CP) be x.
So initial selling price (SP) will be 110% of x = 11x/10.
Now, new CP = x+20
New SP = 11x/10 + 10
New profit = New SP - New CP
= 11x/10 + 10 - x - 20
= x/10 - 10
Profit percentage = New profit/ New CP x 100
= (x/10 - 10).100 / (x + 20)
= 10(x-100) / (x + 20)
Equating it with 10/9 % as given in the question:
10(x-100)/(x+20) = 10/9
=> 9(x-100) = x+20
=> 9x - 900 = x + 20
=> 8x = 920
=> x = 920/8 = 115
So the original cost price was Rs 115.
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