Sum of the digits of a two digit no.is 9.When we interchange the digits,it is found that the resulting new no.is greater than the original no.by 27.What is the two digit no.?

Question

Answer

Let the digit at unit place the x
the digit at tens place be 3x
the no. =10(3x)+x=30x+x=31x
on interchanging the digit the number will be
10x +3x = 13x

according to the condition we have 31x +13x=88
=44x=88
=x=2

the no. = 31×2= 62

Answer

Find the two digit number when interchanged the difference is 27 and sum of two digits are 9

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Answer

Problem:
The sum of the digits of a two-digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two-digit number?

Solution:

To solve this problem, we need to find a two-digit number that satisfies two conditions:
1. The sum of its digits is 9.
2. The new number formed by interchanging the digits is greater than the original number by 27.

Let's assume the original two-digit number as '10x + y' where x is the tens digit and y is the units digit. From the first condition, we know that x + y = 9.

Understanding the Second Condition:
According to the second condition, when we interchange the digits, the resulting new number is greater than the original number by 27. This can be expressed as:
(10y + x) - (10x + y) = 27

Simplifying the expression, we get:
10y + x - 10x - y = 27
9y - 9x = 27
y - x = 3

Using Simultaneous Equations:
Now, we have two equations:
1. x + y = 9
2. y - x = 3

We can solve these two simultaneous equations to find the values of x and y.

Adding equation 1 and equation 2, we get:
2y = 12
y = 6

Substituting the value of y in equation 1, we get:
x + 6 = 9
x = 3

Therefore, the tens digit (x) is 3 and the units digit (y) is 6. The two-digit number is 36.

Conclusion:
The two-digit number that satisfies both conditions is 36. The sum of its digits is 9, and when the digits are interchanged, the resulting new number is 63, which is 27 greater than the original number.

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