Question

plzz solve this two question

1. The units digit of a two-digit number is 3 and seven times the sum of the digits is the
number itself. Find the number.


2. In a two-digit number, the digit at the units place is double the digit in the tens place. The number
exceeds the sum of its digits by 18. Find the number.
A wo digit number is 3 more than 4 times the sum of its digits If is is added to the​

Answer 1

Answer 1.

Number = 63

__________________

Explanation

Let ten's digit be x and unit digit be y.

$\therefore$ Number = 10x + y

According to question

The units digit of a two-digit number is 3

⇒ y = 3 ___ (eq 1)

Seven times the sum of the digits is the

number itself.

⇒ 7(x + y) = 10x + 3

⇒ 7x + 7(3) = 10x + 3 [From (eq 1)]

⇒ 7x - 21 = 10x + 3

⇒ 10x - 7x = - 3 + 21

⇒ 3x = 18

⇒ x = 6

•°• Number = 10x + y

⇒ 10(6) + 3

⇒ 60 + 3

⇒ 63

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Answer 2.

Number = 24

_____________________

Explanation

Let ten's digit number be x and unit digit number be y.

$\therefore$ Number = 10x + y

According to question

The digit at the units place is double the digit in the tens place.

⇒ y = 2x ___ (eq 1)

The number exceeds the sum of its digits by 18.

⇒ 10x + y = x + y + 18

⇒ 10x - x + y - y = 18

⇒ 9x = 18

⇒ x = 2

Put value of x in (eq 1)

⇒ y = 2(2)

⇒ y = 4

Number = 10x + y

⇒ 10(2) + 4

⇒ 24

Answer 2

$\bold{\underline{\underline{Answer:}}}$

Number = 63

$\bold{\underline{\underline{Step\:by\:step\:explanation:}}}$

Given :

• The units digit of a two-digit number is 3
• Seven time the sum of the digits is the number itself.

To find :

• The Number.

Solution :

Let the digit in the tens place be x.

The units digit = 3. [Given]

Original number = 10x + 3

$\bold{\underline{\underline{As\:per\:the\:given\:condition:}}}$

• Seven time the sum of the digits is the number itself.

Constituting it mathematically,

$\rightarrow$ $\bold{7(x+3)=10x+3}$

$\rightarrow$ $\bold{7x+21=10x+3}$

$\rightarrow$ $\bold{7x-10x=3-21}$

$\rightarrow$ $\bold{-3x=-18}$

$\bold{x={\dfrac{-18}{-3}}}$

$\bold{x={\dfrac{18}{3}}}$

$\bold{x=6}$

$\bold{\boxed{\large{\rm{\sf{Tens\:digit\:=\:x=6}}}}}$

$\bold{\boxed{\large{\rm{\sf{Units\:digit\:=\:y=3}}}}}$

$\bold{\boxed{\large{\rm{\sf{Original\:Number\:=\:10x\:+\:3=\:10\times\:6+3\:=\:60\:+\:3\:=\:63}}}}}$

______________________________

$\bold{\underline{\underline{Answer:}}}$

Number = 24

$\bold{\underline{\underline{Step\:by\:step\:explanation:}}}$

Given :

• In a two-digit number, the digit at the units place is double the digit in the tens place.
• The number exceeds the sum of its digits by 18.

To find :

• The number.

Solution :

Let the digit in the tens place be x.

Let the digit in the units place be y.

Original number = 10x + y

$\bold{\underline{\underline{As\:per\:the\:given\:condition:}}}$

• The digit at the units place is double the digit in the tens place.

Constituting it mathematically,

$\bold{y=2x}$ ---> (1)

$\bold{\underline{\underline{As\:per\:the\:second\:given\:condition:}}}$

• The number exceeds the sum of its digits by 18.

Constituting it mathematically,

$\rightarrow$ $\bold{10x+y=x+y+18}$

$\rightarrow$ $\bold{10x-x=y-y +18}$

$\rightarrow$ $\bold{9x=18}$

$\rightarrow$ $\bold{x={\dfrac{18}{9}}}$

$\bold{x=2}$

Substitute x = 2 in equation 1,

y = 2x

y = 2(2)

y = 4

$\bold{\boxed{\large{\rm{\sf{Tens\:digit\:=\:x=2}}}}}$

$\bold{\boxed{\large{\rm{\sf{Units\:digit\:=\:y=4}}}}}$

$\bold{\boxed{\large{\rm{\sf{Original\:Number\:=\:10x\:+\:y=\:10\times\:2+4\:=\:20\:+\:4\:=\:24}}}}}$