Question

A number consists of two digits. When the number is divided by the sum of its digits, the quotient is 7. If 27 is subtracted from the number, the digits interchange their places, find the number. ​

Answer 1

Answer:

As the no. is of two digits:-

◕Let us take x at ten's place and y at one's.

So we get :- 10x + y

According to the question:-

✨ A no. consisting of two digit is 7 times the sum of its digit.

$\: \: \: \: \: \: \: \: \: \: \: 10x + y \: = 7(x + y) \\ = > \: \: \: \: 3x - 6y = 0 \\ = > \: \: \: \: \: \: \: \: \: \: \: \: \: \: \ \: x = 2y \: \: \: \: ......(1)$

Now, when 27 is subtracted the no. get reversed.

✧ So we get :- 10y + x

$\: \: \: \: \: \: \:( 10x + y) - 27 = 10y + x \\ = > \: \: \: \: \: \: \: \: \: \: \: \: 9x - 9y = 27 \\ = > \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x - y = 3 \: ......(2)$

● Put the value of x from eq ( 1 ) to eq ( 2 ) :-

$\: \: \: \: \: \: \: \: \: 2y - y = 3 \\ = > \: \: \: \: \: \: \: \: \: \: \: y = 3$

So , x = 2y

=> x = 2 (3) = 6

So, the required no. is 63✨

Hope it helped ✌️ ✌️

Answer 2

Step-by-step explanation:

let unit digit=x

let unit digit=xtens digit=y

let unit digit=xtens digit=ynumber=10y+x

let unit digit=xtens digit=ynumber=10y+x(10y+x)/x+y =7 (1)

let unit digit=xtens digit=ynumber=10y+x(10y+x)/x+y =7 (1)10y+x-27=10x+y

let unit digit=xtens digit=ynumber=10y+x(10y+x)/x+y =7 (1)10y+x-27=10x+y9y-9x-27=0

let unit digit=xtens digit=ynumber=10y+x(10y+x)/x+y =7 (1)10y+x-27=10x+y9y-9x-27=0y-x-3=0

let unit digit=xtens digit=ynumber=10y+x(10y+x)/x+y =7 (1)10y+x-27=10x+y9y-9x-27=0y-x-3=0from (1) 10y+x=7x+7y

let unit digit=xtens digit=ynumber=10y+x(10y+x)/x+y =7 (1)10y+x-27=10x+y9y-9x-27=0y-x-3=0from (1) 10y+x=7x+7y3y=6x

let unit digit=xtens digit=ynumber=10y+x(10y+x)/x+y =7 (1)10y+x-27=10x+y9y-9x-27=0y-x-3=0from (1) 10y+x=7x+7y3y=6xy=2x

let unit digit=xtens digit=ynumber=10y+x(10y+x)/x+y =7 (1)10y+x-27=10x+y9y-9x-27=0y-x-3=0from (1) 10y+x=7x+7y3y=6xy=2x2x-x-3=0

let unit digit=xtens digit=ynumber=10y+x(10y+x)/x+y =7 (1)10y+x-27=10x+y9y-9x-27=0y-x-3=0from (1) 10y+x=7x+7y3y=6xy=2x2x-x-3=0x=3,y=6

number =63

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