Math, asked by reet2200, 11 months ago

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

Answered by abhi569
33

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.

Answered by suman682
50

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.

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