Question

find two number thought by me the digit at the tens place is 5 less than twice the digit at unit place the sum of the original number and the number obtained by interchanging the digit is 176 let the digit at the tens place be x and digit at the unit place be y for the number thought

Answer 1

Putting is value of y in equation 1,
x=9

Original number is 97.



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Answer 2

$\bold{\underline{\underline{\huge{\sf{ANSWER\::}}}}}$

Given:

The digit at tens place is 5 less than twice the digit at units place. The sum of the original number and the number number obtained by interchanging the digits is 176.

To find:

The two digit number.

Explanation:

We have,

Let the digit at ten's place be x &

Let the digit at unit's place be y.

A/q,

→ x= 5 -2y

→ 2y -x =5...........................(1)

∴The original number= 10x + y

The interchange number= 10y + x

When number obtained by interchanging the digits is 176.

→ 10x + y + 10y + x = 176

→ 11x + 11y = 176

→ 11(x+y)= 176

→ x+y= $\cancel{\frac{176}{11} }$

→ x+y= 16..............................(2)

• Using Substitution Method:

From equation (1),we get;

⇒ 2y -x= 5

⇒ 2y= 5+x

⇒ y= $\frac{5+x}{2} ..........................(3)$

Putting the value of y in equation (2), we get;

⇒ x+ $(\frac{5+x}{2} )$ = 16

⇒ 2x+5+x= 32

⇒ 3x+5=32

⇒ 3x= 32-5

⇒ 3x= 27

⇒ x= $\cancel{\frac{27}{3} }$

⇒ x= 9

&

Putting the value of x in equation (3),we get;

⇒ y= $\frac{5+9}{2}$

⇒ y= $\cancel{\frac{14}{2} }$

⇒ y= 7.

Thus,

The original number= 10(9)+7

The original number= 90+7

The original number= 97.