Question

Find the two digit number. Let digit at tens place be x and units place be y.


The digit at tens place is 5less than twice the digit at units place .


The sum of the original number and the number obtained by interchanging the digits is 176

Answer 1

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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.