P sold his bicycle to Q at a profit of 10%.Q sold it to R for #209 at a loss of 5%.how much did the bycycle cost?

Please explain well thanks tutor

Do you mean he sold it for $209.00?

yes misue

0.95x = 209

x = 220

R paid $220 for it.

1.1x = 220

x = 200

Q paid $200.

To find the cost of the bicycle, we need to reverse the process by calculating the original selling prices.

Let's start by finding the selling price at each stage:

1. P sells the bicycle to Q at a profit of 10%
Let's assume the cost price of the bicycle to P is x.
So, P sells the bicycle to Q at a price of (x + 10% of x).

2. Q sells the bicycle to R at a loss of 5%
Q sells the bicycle to R at a price of #209, which is 5% less than the selling price to R.
Let's assume the selling price to Q was y.
Therefore, #209 = (y - 5% of y).

Now, let's solve the equations to find the values of x and y.

1. P sells the bicycle to Q at a profit of 10%:
Selling price = (x + 10% of x) = (x + 0.10x) = 1.10x

2. Q sells the bicycle to R at a loss of 5%:
Selling price = y
Selling price - 5% of Selling price = y - 0.05y = 0.95y

We know that Q sold the bicycle to R for #209, so 0.95y = #209.

To find y, divide both sides of the equation by 0.95:
y = #209 / 0.95

Now that we know the value of y, we can find x.

We are given that P sells the bicycle to Q, so 1.10x = y.
Substituting the value of y, we have:
1.10x = #209 / 0.95

To find x, divide both sides of the equation by 1.10:
x = (#209 / 0.95) / 1.10

Now, substitute the values of y and x in the respective equations to find the cost of the bicycle:

Cost of the bicycle = x

Therefore, the cost of the bicycle is (#209 / 0.95) / 1.10.