A shopkeeper sold a certain (a two digit number) of toys all priced at a certain value
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number of toys sold: let's make the number ab, where a is the 10th digit and b is the first digit.
So that value is 10a + b (example if the number was 34, that can be expressed as 10(3) + 4 = 34)
price of each item: xy
10x + y
He accidentally reversed the digits to:
10b + a toys sold at 10y + x rupees per toy.
I don't think that we actually need to use the prices to solve this.
He actually sold 10a + b toys, but thought he sold 10b + a toys.
The number of toys that he thought he left over was 72 items more than the actual amount of toys left over.
So he sold 72 more toys than he thought:
10a + b = 10b + a + 72
9a = 9b + 72
a = b + 8
The only numbers that could work are a = 9 and b = 1 since a and b each have to be 1-digit numbers.
So the actual number of toys sold was 10a + b = 10(9) + 1 = 91
He sold 91 toys.
He reversed the digits
so he thought he sold 19 toys
So he sold 91 - 19 = 72 toys more than the amount that he Thought he sold. As a result, the number of toys he thought he left over was 72 more than the actual amount left over, as per the question.
So that confirms that he actually sold 91 toys.
-Hope it helps you.
So that value is 10a + b (example if the number was 34, that can be expressed as 10(3) + 4 = 34)
price of each item: xy
10x + y
He accidentally reversed the digits to:
10b + a toys sold at 10y + x rupees per toy.
I don't think that we actually need to use the prices to solve this.
He actually sold 10a + b toys, but thought he sold 10b + a toys.
The number of toys that he thought he left over was 72 items more than the actual amount of toys left over.
So he sold 72 more toys than he thought:
10a + b = 10b + a + 72
9a = 9b + 72
a = b + 8
The only numbers that could work are a = 9 and b = 1 since a and b each have to be 1-digit numbers.
So the actual number of toys sold was 10a + b = 10(9) + 1 = 91
He sold 91 toys.
He reversed the digits
so he thought he sold 19 toys
So he sold 91 - 19 = 72 toys more than the amount that he Thought he sold. As a result, the number of toys he thought he left over was 72 more than the actual amount left over, as per the question.
So that confirms that he actually sold 91 toys.
-Hope it helps you.
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