Two digit number is divisible by 9 Number when multiplied by sum of its digit is equal to 486 - Maths - Pair of Linear Equations in Two Variables

Question

Two digit number is divisible by 9 Number when multiplied by sum of
its digit is equal to 486 Given digits are unequal, find the number

Anuradha Sharma · Accepted Answer

since a two digit number can be written as 10x+y where x and y are
required numbers

sum of digits is x+y and it gets multiplied by number which is
10x+y

so (x+y)(10x+y)=486

now when a number is divisible by 9 , the sum of digits of the
number is 9

( 18 =>1+8=9, 27=> 2+7=9, 36=>3+6=9, 54=> 5+4=9 and so
on )

so we have sum of digits as x+y=9

using in above equation (9)(10x+y)=486

=> 10x+y = 54 ( dividing both side by 9)

now solve these two equations

x+y=9

10x+y=54

subtracting both we have (10x+y)-(x+y)=54-9

9x = 45

x= 5

so y=9-x=9-5=4

hence number is 5x10+4=54

Two digit number is divisible by 9. Number when multiplied by sum of its digit is equal to 486. Given digits are unequal, find the number.