the sum of the digits of a two digit number is 12. if the digits are reversed,the new number is 4/7 times the original number. determime the original number.
Answers
Answer:
Required number is 84.
Step-by-step explanation:
Let,
Required two digit number be ab, which can be written as 10a + b. Here 'a' is at unit's place and b is at one's place. In fact all the two digit numbers can be written in this form.
Given,
Sum of the digits is 12.
= > Digit at unit's place + digit at one's place = 12
= > a + b = 12
= > a = 12 - b ...( 1 )
According to the question : If the digits are reversed, the new number is 4/7 times the original number.
Thus,
= > Number with reversed digits = 4 / 7 x original number
= > 10b + a = 4 / 7 x ( 10a + b ) { Now b and a have changed their places }
= > ( 10b + a )7 = 4( 10a + b )
= > 70b + 7a = 40a + 4b
= > 70b - 4b = 40a - 7a
= > 66b = 33a
= > 66b = 33( 12 - b ) { from ( 1 ) }
= > 66b = 396 - 33b
= > 66b + 33b = 396
= > 99b = 396
= > b = 396 / 99
= > b = 4
Thus,
= > a = 12 - b
= > a = 12 - 4
= > a = 8
Therefore the required number is 84.
Let the number be xy .
it can also be expressed as
10x+y . x+y=12 .
when reversed it becomes y-x and can be expressed as 10y+x. 10y+x=4/7(10x+y)
=> 7(10y+x)=4(10x+y) =>70y+7x=40x+4y
=>70y-4y=40x-7x
=>66y=33x
=> 2y=x
2y+y=12
=> 3y=12
=> y=4
x=2y=2(4)=8.
So the original number is 8(10)+4=84.