The cost of a bat is a two digit number (for example $xy). Its selling prices has same digits as cost with digits interchanged ($yx). If its profit margin is divided by 9, find the remainder of division.
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Step by Step Explanation:
- Let the cost of bat is $xy . Another way of depicting the cost is 10x + y .
- So the selling price of the bat will be $yx. Another way of depicting the selling price is 10y + x .
- So the profit is Selling Price - Cost price . The difference between the two prices would be 9x-9y or 9y-9x . So the price would be 9(x-y) or 9(y-x) , which would be a multiple of 9 .
- Therefore the remainder when divided by 9 will always be 0.
For example - if cost is $46 , then selling price will be $64 .
So profit will be 64-46 = 18. Since 18 is a multiple of 9 , so the remainder when divided by 9 will be 0 .