Answer:
The cost price is Rs.500
Explanation:
I'll approach this question by taking the statements in the question, one after the other
Let the cost price be represented by CP
From the first statement:
Sanjay made a loss of 25%
The selling price (SP) is as follows;
[tex]SP = CP - 25\% * CP[/tex]
Convert percent to fraction
[tex]SP =CP - \frac{25}{100} * CP[/tex]
Get decimal equivalent
[tex]SP = CP-0.25 * CP[/tex]
[tex]SP = CP - 0.25CP[/tex]
[tex]SP = 0.75CP[/tex]
From the second statement:
If the selling price was increased by 175%, Sanjay would make a profit of 10%
Hence; The new selling price is
[tex]SP = 0.75CP + 175[/tex]
The selling price can also be calculated from the profit
[tex]SP = CP + 10\% * CP[/tex]
Convert percent to fraction
[tex]SP = CP + \frac{10}{100} * CP[/tex]
Get decimal equivalent
[tex]SP = CP + 0.10 * CP[/tex]
[tex]SP = CP + 0.10 CP[/tex]
[tex]SP = 1.10 CP[/tex]
Equate both values of SP (SP = SP)
[tex]1.10CP = 0.75CP + 175[/tex]
Collect Like Terms
[tex]1.10CP - 0.75CP = 175[/tex]
[tex]0.35CP = 1.75[/tex]
Divide both sides by 0.35
[tex]CP = \frac{175}{0.35}[/tex]
[tex]CP = 500[/tex]
Hence, the cost price is Rs.500
