Question

The cost of a pen is a two-digit number. Its selling price has the same digits as cost price with digits interchanged. If its profit margin is divided by 9. Find the remainder of the division.

Answer 1

Hint: Let the ones digit of the cost price be x and the tens digit of the cost price be y. So, the cost price is equal to Rs. (10y+x) while the selling price will be Rs. (10x+y). Once you know the selling price and the cost price, find the difference between them to get the profit, as Profit = selling price – cost price. Now that you have the profit, divide it by 9 and find the remainder.

Complete step-by-step answer:
Let us start by letting the ones digit of the cost price be x and the tens digit of the cost price be y. So, the cost price of the pen will be Rs. (10y+x). Also, it is given that selling price has the same digits as cost price with digits interchanged. So, the tens digit of the selling price is x and the ones digit is y. So, the selling price is Rs. (10x+y)
Now we know that the profit is the difference between the cost price and the selling price. We know Profit = selling price – cost price. So, substituting the values according to our assumption, we get
Profit = selling price – cost price
Profit = 10x+y – (10y+x)
Profit = 9x-9y.
If we take 9 common, we get
Profit = 9(x-y)
As 9 is a factor of profit margin, it is divisible by 9 and we know that a number is divisible by a factor if it leaves remainder zero when divided by the factor.
So, we can say that if its profit margin is divided by 9 the remainder is zero.

Note: Don’t get confused and consider the cost price to be Rs. yx, where y is a digit and x is another digit, because this will mean that the cost price is equal to the product of y and x while the cost price is actually equal to Rs. (10y+x). Also, remember that if the profit is negative, the absolute value of profit is the loss taken by the seller. Often students forget that 9(x-y) means that 9 is a factor of profit margin and they write the remainder as (x-y).