Answer:
The cost price is Rs.500
Explanation:
<em>I'll approach this question by taking the statements in the question, one after the other</em>
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;
![SP = CP - 25\% * CP](https://tex.z-dn.net/?f=SP%20%3D%20CP%20-%2025%5C%25%20%2A%20CP)
Convert percent to fraction
![SP =CP - \frac{25}{100} * CP](https://tex.z-dn.net/?f=SP%20%3DCP%20-%20%20%5Cfrac%7B25%7D%7B100%7D%20%2A%20CP)
Get decimal equivalent
![SP = CP-0.25 * CP](https://tex.z-dn.net/?f=SP%20%3D%20CP-0.25%20%2A%20CP)
![SP = CP - 0.25CP](https://tex.z-dn.net/?f=SP%20%3D%20CP%20-%200.25CP)
![SP = 0.75CP](https://tex.z-dn.net/?f=SP%20%3D%200.75CP)
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
![SP = 0.75CP + 175](https://tex.z-dn.net/?f=SP%20%3D%200.75CP%20%2B%20175)
The selling price can also be calculated from the profit
![SP = CP + 10\% * CP](https://tex.z-dn.net/?f=SP%20%3D%20CP%20%2B%2010%5C%25%20%2A%20CP)
Convert percent to fraction
![SP = CP + \frac{10}{100} * CP](https://tex.z-dn.net/?f=SP%20%3D%20CP%20%2B%20%5Cfrac%7B10%7D%7B100%7D%20%2A%20CP)
Get decimal equivalent
![SP = CP + 0.10 * CP](https://tex.z-dn.net/?f=SP%20%3D%20CP%20%2B%200.10%20%2A%20CP)
![SP = CP + 0.10 CP](https://tex.z-dn.net/?f=SP%20%3D%20CP%20%2B%200.10%20CP)
![SP = 1.10 CP](https://tex.z-dn.net/?f=SP%20%3D%201.10%20CP)
Equate both values of SP (SP = SP)
![1.10CP = 0.75CP + 175](https://tex.z-dn.net/?f=1.10CP%20%3D%200.75CP%20%2B%20175)
Collect Like Terms
![1.10CP - 0.75CP = 175](https://tex.z-dn.net/?f=1.10CP%20-%200.75CP%20%3D%20175)
![0.35CP = 1.75](https://tex.z-dn.net/?f=0.35CP%20%3D%201.75)
Divide both sides by 0.35
![CP = \frac{175}{0.35}](https://tex.z-dn.net/?f=CP%20%3D%20%5Cfrac%7B175%7D%7B0.35%7D)
![CP = 500](https://tex.z-dn.net/?f=CP%20%3D%20500)
<em>Hence, the cost price is Rs.500</em>