Please Help Me :( Aaya 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%. If he gained 7% on his total outlay, at what price
did he buy each item?

Please Help Me :(

The fan = x = 400

The heater = y = 3600

Step-by-step explanation:

Let the cost price of

The fan = x

The heater = y

Aaya bought a fan and a heater for Rs 4,000.

x + y = 4000

x = 4000 - y

He sold the fan at a profit of 25%

25% × x = 0.25x

And the heater at a loss of 5%.

5% × x = 0.05y

If he gained 7% on his total outlay, at

Hence:

0.25x + 0.05y = 7% × 4,000

0.25x + 0.05y = 280

Note:

x = 4000 - y

Hence:

0.25(4000 - y) + 0.05y = 280

1000 - 0.25y + 0.05y = 280

Collect like terms

-0.25y + 0.05y = 280 - 1000

-0.20y = -720

y = -720/0.20

y = 3600

x = 4000 - y

x = 4000 - 3600

x = 400

Hence, the price that he bought each item is given as:

The fan = x = 400

The heater = y = 3600

the 8 in 8,420 is in the thousands place so it's value is 8 thousand.

the 8 in 6,870 is in the hundreds place so it's value is 8 hundred.

divide 8000 by 800 to find the answer:

8000 / 800 = 10

the 8 in 8,420 is 10 times greater than the 8 in 6,870