Question

The sum of a two digit number and the numerator formed by interchaning the digit is 110.If 10 is subtracted from the first number, the new number is 4 more than 5 times the sums of the digits of the first number. Find the first number​

Answer 1

Answer:-

●Solution:-

☆Let the one's digit be x and ten's digit be y.

☆Number= (10y+x)

☆Exchanged number= (10x+y)

★According to question:-

(10y+x)+(10x+y)=110

or, 10y+x+10x+y=110

or, 11y + 11x =110

or, 11(x+y)=110

or, x+y=110/11

or, x+y=10

Then, x =10-y...............(i)

Then, y = 10-x..............(ii)

★ According to question:-

(10y+x)-10 = 4 + 5 (y+x)

or, 10y+x-10=4+5y+5x

or, 10y-5y+x-5x=4+10

or, 5y-4x=14

Putting the value of y here,

5(10-x)-4x=14

or, 50-5x-4x =14

or, -9x =14-50

or, -9x =-36

or, x =-36/-9

So, X =4

Putting the value of x in the (ii) equation,

y = 10-4 [x =4]

So, y =6

So, the first number =10y+x

First number =10 × 6+4

The first number=60+4

So, the first number =64

Hope it helps you ★ ★ ★

Answer 2

$\huge\sf{Answer}$

• Let the Ones Digit be x 

• Tens Digit be y.

▪Number which will be = (10y + x)

▪Number which will be Formed by Interchange = (10x+ y)

⇒ (10y + x) + (10x + y) = 110

⇒ 11y + 11x = 110

⇒ 11(y + x) = 110

Dividing the terms by 11

⇒ y + x = 10 ⠀⠀⠀⠀⠀⠀⠀⠀⠀

⇒ x = 10 - y ⠀⠀⠀⠀⠀⠀⠀⠀⠀

⇒ 10 = 4 + 5 × [Sum of digists]

⇒ (10y + x) - 10 = 4 + 5 × (y + x)

⇒ 10y + x - 10 = 4 + (5 × 10)

⇒ 10y + x - 10 = 4 + 50

⇒ 10y + x = 54 + 10

putting the value of x from equation number 1

⇒ 10y + 10 - y = 54 + 10

⇒ 10y - y = 54 + 10 - 10

⇒ 9y = 54

Dividing the terms by 9

⇒ y = 6

Now, we Putt the Value of y in equation 2

⇒ x = 10 - y

⇒ x = 10 - 6

⇒ x = 4

Therefore

(10y + x)

10(6) + 4

60 + 4

64

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