Given :
Ajaya bought a fan and a heater for Rs 4,000. He sold the fan at a profit of 25% and the heater at a loss of 5%.
To Find :
If he gained 7% on his total outlay, at what price did he buy each item.
Solution :
Let, cost price of fan and heater is x and y respectively.
x + y = 4000 ....1)
Price of fan after 25% profit, x + 0.25x = 1.25x .
Price of heater after 5% loss, y - 0.07y = 0.93y .
Total profit, 4000 + 0.07×4000 = 4000×1.07 = $4280 .
Equation of selling price :
1.25x + 0.93y = 4280 ....2)
Putting value x from of 1) in equation 2), we get :
[tex]1.25(4000-y ) +0.93y = 4280\\\\5000 - 1.25y + 0.93y = 4280\\\\0.32y = 720\\\\y = Rs\ 2250[/tex]
So, x = 4000 - 2250
x = Rs 1750
Therefore, he buy fan for Rs 2250 and heater for Rs 1750.
