Question

the ratio of a 2 digit number to to the sum of its digit is 7:1 if the digit in tens place is 1 more than the digit in the ones place then the number is

Answer 1

Correct Question:-

The ratio between two digit number and the sum of the digits is 7:1. If the digit in ten's place is 1 more than the digit in the one's place, then the new number is?

Solution:-

Let ten's digit be M and one's digit be N.

Sum of digits = M + N

Two digit number = 10M + N

According to question,

⇒ $\sf{\dfrac{10M\:+\:N}{M\:+\:N}\:=\:\dfrac{7}{1}}$

⇒ $\sf{10M\:+\:N\:=\:7(M\:+\:N}$

⇒ $\sf{10M\:+\:N\:=\:7M\:+\:7N}$

⇒ $\sf{10M\:-\:7N\:=\:7N\:-\:N}$

⇒ $\sf{3M\:=\:6N}$ ___ (eq 1)

Digit in ten's place is 1 more than the digit in the one's place.

So,

⇒ $\sf{M\: =\: N\: +\: 1}$

Substitute value of M in (eq 1)

⇒ $\sf{3(N\:+\:1)\:=\:6N}$

⇒ $\sf{3N\:+\:3\:=\:6N}$

⇒ $\sf{3N\:=\:3}$

⇒ $\sf{N\:=\:1}$

Now,

⇒ $\sf{3M\:=\:6(1)}$

⇒ $\sf{3M\:=\:6}$

⇒ $\sf{M\:=\:2}$

Number = 10M + N

⇒ $\sf{10(2)\:+\:1}$

⇒ $\sf{20\:+\:1}$

⇒ $\bold{\sf{21}}$

Answer 2

$\huge{\star}{\underline{\boxed{\red{\sf{Answer :-}}}}}{\star}$

Let ten's digit andbone's digit be x and y respectively.

Sum of digits = x + y

Two digit number = 10x + y

A.T.Q

10x + y / x + y = 7 / 1

★ By cross multiplication

10x + y = 7(x + y)

10x + y = 7x + 7y

★ Taking x term to LHS and y term to RHS

10x − 7y =7x - y

→ 3M = 6N ________[1]

So,

A.T.Q

x = y + 1

Put value of x in (1)

3(y + 1) = 6y

3y + 3 = 6y

3y = 3

→ y = 1

$\huge{\boxed{\pink{\sf{y = 1}}}}$

Now,

Put value of y in equation 1

3x = 6(1)

3x = 6

→ x = 2

$\huge{\boxed{\pink{\sf{x = 2}}}}$

Number = 10x + y

→ 10(2)+1

→ 20+1

→ 21

$\huge{\boxed{\pink{\sf{Number = 21}}}}$