Question

A sells a bicycle to B at a profit of 20% and B sells it to C at a profit of 25%, If C pays Rs. 1500, what did A pay for it?

Answer 1

Hint: Let the cost price of A be Rs. x and the cost price of B be Rs. y. Use the formula to form two equations using the statements given in the question, one for the statement that A sells a bicycle to B at a profit of 20% and other for the statement that B sells it to C at a profit of 25% . Sole the two equations to get the value of x.

Complete step-by-step answer:
Let us start the solution to the above question by letting the cost price of A be Rs. x and the cost price of B be Rs. y. Also, we know that A sold the bicycle to B so, cost price of B is actually equal to the selling price of A and the selling price is equal to the cost price added with profit. It is given that the profit of A is 20%. So, combining all this data, we get
$selling\text{ }price=\cos t\text{ }price\text{ }+\text{ }profit.$
$\Rightarrow y=x\text{ }+\text{ }\dfrac{20}{100}\times x=\dfrac{120x}{100}.......(i)$
It is also given that the B sold it to C for a profit of 25% at a price of Rs. 1500. So, if we represent this mathematically we get
$selling\text{ }price=\cos t\text{ }price\text{ }+\text{ }profit.$
$\Rightarrow 1500=y\text{ }+\text{ }\dfrac{25}{100}\times y=\dfrac{125}{100}y$
Now we will use equation (i) to substitute the value of y. On doing so, we get
$1500=\dfrac{125}{100}\times \dfrac{120}{100}\times x$
$\Rightarrow 1500=\dfrac{5}{4}\times \dfrac{6}{5}\times x$
$\Rightarrow 1500=\dfrac{3}{2}\times x$
$\Rightarrow x=Rs.\text{ }1000$
Hence, the answer to the above question is Rs. 1000.

Note: Remember that the profit of B is with respect to his cost price, i.e., y, so don’t get confused and calculate the profit of B with respect to cost price of A, i.e., x. Also, it is a key point that the selling price of A is equal to the cost price of B and you cannot solve the question without it.