A two-digit number is 3 more than 4 times the sum of its digits. If 18 is added to the number, its digits are reversed. Find the number.

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The number is 35. The numbers should be x and y.

According to the question, number=10x+y

Now, According to the question we can write as:

(10x+y) – 4(x+y)= 3…..(i)

According to the question we can write as:

(10x+y)+ 18=10y+x…..(ii)

Solving equation (i)

10x+y-4x-4y=3

or,6x-3y=3

In simplification we get the:

2x-y=1….(1)

Solving (ii)

10x+y-10y-x=-18

or, 9y-9x=18

In simplification we get the:

y-x=2…(2)

Now by adding equations we get:

(1)+(2)

2x-y+y-x=1+2

or,x=3

Thus, y=x+2 (from (2))

y=5

Therefore the number= 10x+y=10×3+5=35

Table of content

1. A two-digit number is 3 more than 4 times the sum of its digits. If 18 is added to the number, its digits are reversed. Find the number.

Properties of Numbers

A number is an arithmetic value that is used to calculate and represent a quantity. Numerical symbols, such as 3, are written to represent numbers. A number system is a logical way of writing numbers that use digits or symbols to represent them. the system of numbers

a helpful collection of numbers
that reflects the number’s algebraic and mathematical structure.
offers a common depiction.

Real numbers are simply where the qualities of numbers are stated. The following traits are common:

Commutative Property
Associative Property
Distributive Property
Closure Property
Identity Property
Additive Inverse
Multiplicative Inverse
Zero Product Property
Reflexive Property

Summary: