Question

The sum of two digits and the number formed by interchanging its digit is 110. If ten is subtracted from the first number, the new number is 4 more than 5 times of the sum of the digits in the first number. Find the first number.​

Answer 1

Given :

The sum of two digits and the number formed by interchanging its digit is 110. If ten is subtracted from the first number, the new number is 4 more than 5 times of the sum of the digits in the first number. Find the first number.

To Find :

• The first number

Solution :

Let us assume :

The unit digit be x

The tens digit be y

According to the question :

Then the sum will be 10y + x

But we are informed that the digits are interchanged : 10x + y

Given Information :

1st Case :

Sum of both the numbers is 110

It means that we need to add the original digit with the interchanged one to get 110

• 10y + x + 10x + y = 110

• 11x + 11y = 110

By factorising we get 11 as common

• 11(x + y) = 110

• x + y = 10

• x = 10 - y -------- eq(1)

2nd Case :

It is given that 10 is subtracted from first number i.e. 10y + x after that the number is 4 more the sum of digits in the first number i.e. x + y.

Hence, the equation we got is :

• 10y + x - 10 = 4 + 5(x + y)

• 10y + x - 10 = 4 + 5x + 5y

• 10y - 5y + x - 5y = 4 + 10

• 5y - 4x = 14 ------ eq(2)

Now, by substitution method from simultaneous linear equations

Putting x = 10 - y in eq(2) we get

• 5y - 4(10 - y) = 14

• - 5y - 4y = 14 + 40

• 9y = 54

• y = 6

As we got the value of y we will now proceed to find the value of x

Putting y = 6 in eq(1) we get

• x = 10 - 6

• x = 4

Then as we got the first number as 10y + x we will put the value of both the variables

• 10 × 6 + 4

• 60 + 4

• 64

Therefore, the first number is 64