# Word Problem 3

**Problem 3 : A sells a house to B at profit of 5% and B sells it to C at profit of 10%. If C pays Rs 231 for it, what did it cost to A ?**

**Solution:**

Here we have to find the cost price which A paid for it

We take A, B and C’s cases individually:

**A’s Case:**

Suppose cost price (CP) for A is x. Given here that A earns 5% profit i-e profit is 5% of cost price.

Since A is earning profit, We use Profit formula here which is;

Putting values of P (profit) and CP (cost price)

From there we can get sale price SP for A

Or

Now this sale price will become cost price for B

**B’s Case**

B also earned profit, we again use here profit formula.

Given in question that B earns 10% profit of his cost price so,

Taking -ve term to other side;

Or

After simplification, we get sale price for B as;

Now this sale price of B will become cost price of C

**C’s Case**

We are given that C pays Rs 231 to B i-e cost price of C is Rs. 231. But we found C’s cost price to be

Both are cost price for C , so these should be equal;

i-e

**So, A’s cost was Rs 200/-**