Question

The average of 20 two digit numbers is x. When one of the number n is reversed,the average becomes 3.6+x. What is the difference between the digits in the number n

Answer 1

Answer:

Step-by-step explanation:

According to the question let as consider by mistake he writes 10th number with its digits interchanged

∴10x+y−(10y+x)10=3.6

In these remaining nine numbers are same and they cancel out

10x+y−10y−x10=3.6

9x - 9y = 36

x - y = 4

Answer 2

The difference between the digits in the number n is 8

Given : The average of 20 two digit numbers is x. When one of the number n is reversed , the average becomes 3.6 + x

To find : The difference between the digits in the number n

Solution :

Here it is given that the average of 20 two digit numbers is x

Then sum of 20 two digit numbers = 20x

Let the number n is 10a + b

When the number is reversed then the number becomes 10b + a

After reversing the sum becomes

= 20x - (10a + b) + (10b + a)

= 20x - 10a - b + 10b + a

= 20x - 9a + 9b

Since the average becomes 3.6 + x

So by the given condition

20x - 9a + 9b = 20(3.6 + x)

⇒ 20x - 9a + 9b = 72 + 20x

⇒ 9(b - a) = 72

⇒ b - a = 8

Hence the difference between the digits in the number n is 8

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