The sum of a two-digit number and the number formed by interchanging its digits is 110. If 10 is subtracted from the first number, the new number is 4 more than 5 times the sum of its digits in the first number. Find the first number

The sum of a two-digit number and the number formed by interchanging its digits is 110. If 10 is subtracted from the first number, the new number is 4 more than 5 times the sum of its digits in the first number. Find the first number

1. A
60
2. B
61
3. C
62
4. D
64

Fill Out the Form for Expert Academic Guidance!l

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)

Solution:

let the unit place digit be x and tens place digit be y
then the two-digit number will be 10y + x
and the number formed by interchanging the unit place and tens place digits will be 10x + y
according to the first condition given in the qs i.e, the sum of two numbers is 110 that  is
10y + x + 10x + y = 110
Or, 11x + 11y = 110
divide the above equation by 11 we get
x + y = 10
Or, x = 10 - y ....(i)
now according to the second equation,
if 10 is subtracted from the first number i.e, the new number is 10y + x - 10
given that the new number is 4 more than 5 time the sum of its digits in the first number i.e
the sum of its digits in the first number is x + y, now 5 times of its, 5(x + y), and now 4 more that is, 4 + 5(x + y)
therefore, new number = 4 + 5(x + y)
10y + x - 10 = 4 +5(x + y)
10y - 5y + x = 4 +10 +5x
5y = 14 + 4x.....(ii)
substitute the value of x from (i) to (ii)
we  get , 5y = 14 + 4(10 - y)
5y = 14 + 40 - 4y
y = 6
and from (i)
x = 4
then the first number 10y + x = 10x6 + 4 = 64
The first number is 64.
Hence, the correct option is 4.

Related content

 Area of Square Area of Isosceles Triangle Pythagoras Theorem Triangle Formula Perimeter of Triangle Formula Area Formulae Volume of Cone Formula Matrices and Determinants_mathematics Critical Points Solved Examples Type of relations_mathematics

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)