Question

the sum of the digit of a two digit number is 7 if the digit reversed the. new number incresed by3 less than 4 times the original number . find the original number​

Answer 1

Given :-

• The sum of two digit = 7

• If digit is reversed the new number is increased by 3 which is 4 times less than the original number.

Solution :-

Let the number at unit place be x and the number at tens place be y

Therefore,

Original number = 10x + y

Sum of digits

= x + y = 7 .............eq( 1 )

If we reverse the digit the new number would be increased by 3 which is 4 times less than the original number.

Therefore,

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

10y + x = 40x + 4y - 3

10y + x - 40x - 4y -3

39x - 6y -3 = 0

3( 13x - 2y - 1 ) = 0

13x - 2y = 1 .............eq( 2)

Multiply eq( 1) by 2

2 ( x + y = 7 )

2x + 2y = 14 .......eq( 3)

Adding eq( 2) and eq( 3)

2x + 2y + 13x - 2y = 14 + 1

15x = 15

x = 15/15

x = 1

Put the value of x in eq( 1 )

1 + y = 7

y = 6

Therefore,

The original number will be 10x + y

= 10 * 1 + 6

= 10 + 6

= 16

16 is the original two digit number.

Answer 2

Step-by-step explanation:

Let the ones's digit =x.

So, sum of the digits =7

Tens's digit =7−x

Original no. =10(7−x)+x=70−10x+x=70−9x

Reversed no. =10x+7−x=9x+7

2(orig no) = reversed no. −2

2(70−9x)=9x+7−2

140−18x=9x+5

27x=135

x=5

Ten's digit =7−5=2

No. =25

Hope this is helpful for you.