Ajay bought a fan and a heater for rs 4000. He sold the fan at a profit of a 25% and the heater at a loss of 5%. If he gained 7% on his total outlay at what price did he buy each item?

Respuesta :

Answer: Heater -Rs 2400; Fan- Rs 1600

Step-by-step explanation:

Given

Ajay bought a fan and a heater for Rs 4000

Suppose the price of fan is x and that of heater is 4000-x

Profit on the fan is [tex]0.25x[/tex]

Loss on heater is [tex]0.05\times (4000-x)[/tex]

Total profit is 7% i.e. [tex]0.07\times 4000[/tex]

[tex]\therefore 0.07\times 4000=0.25x-0.05(4000-x)\\\Rightarrow 280=0.25x-200+0.05x\\\Rightarrow 480=0.3x\\\Rightarrow x=1600[/tex]

Thus, the price of heater is [tex]4000-1600=Rs.\ 2400[/tex]

Price of fan is [tex]Rs.\ 1600[/tex]

Price of heater is [tex]Rs.\ 2400[/tex]

The individual cost of fan and heater are;

Cost of fan = Rs. 1600

Cost of heater = Rs. 2400

Total Cost price of heater and fan = Rs 4000

Let cost of fan be x

Thus cost of heater = 4000 - x

Percentage Profit of sale of fan = 25% = 0.25

Loss percentage on heater = 5% = 0.05

Thus;

Profit on fan = 0.25x

Loss on heater = 0.05(4000 - x)

Total profit of all sales = 0.07 × 4000

Thus;

0.07 × 4000 = 0.25x - 0.05(4000 - x)

280 = 0.25x - 200 + 0.05x

480 = 0.3x

x = 480/0.3

x = Rs. 1600

Thus;

Cost of heater = 4000 - 1600

Cost of heater = Rs. 2400

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