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 bicycle cost
P?
first sale: 1.1*C
second sale: 209=.95*1.1*C
C=209/(.95*1.1)=200
Bob Pursley worked this the short way. Here is the long way to do it.
P paid C for the bicycle.
He sold it for C + 0.1 to Q
Q lost 5% when s/he sold it and the selling price was 209 so
C+0.1C - (C+_0.1C)*0.05 = $209
1.045C = 209
C = $200
Check it.
C paid $200.
C sold it to Q for 10% profit or $220.
Q solid it at 5% loss or 220 - 0.05 = $11 loss. Then 220-11 = 209 which is the sale price bv Q.
To find the cost of the bicycle for P, we need to follow these steps:
1. Determine the selling price of Q (the price at which P sold the bicycle to Q).
2. Calculate the cost price of the bicycle for Q (the original price at which Q bought the bicycle from P).
3. Find the selling price of R (the price at which Q sold the bicycle to R).
4. Calculate the cost price of the bicycle for R (the original price at which R bought the bicycle from Q).
5. Deduce the cost of the bicycle for P by reversing the profit percentage from the selling price of Q.
Let's follow these steps:
1. P sold the bicycle to Q at a profit of 10%. Therefore, the selling price of Q can be calculated by increasing the cost price by 10%.
Selling price of Q = Cost price of P + Profit
Let's assume the cost price of P is x.
Profit = 10% of x = (10/100) * x = 0.1x
Selling price of Q = x + 0.1x = 1.1x
2. Q sold the bicycle to R at a loss of 5%. Therefore, the selling price of R can be calculated by decreasing the cost price by 5%.
Selling price of R = Cost price of Q - Loss
Since the selling price of Q is 1.1x, we can calculate the loss as follows:
Loss = 5% of 1.1x = (5/100) * 1.1x = 0.055x
Selling price of R = 1.1x - 0.055x = 1.045x
3. We know that the selling price of R is #209. Therefore, we can set up the following equation:
1.045x = #209
To find the value of x, we need to divide both sides of the equation by 1.045:
x = #209 / 1.045
Simplifying, we find that x = #200.
Therefore, the cost of the bicycle for P is #200.