Question

18. The digit at the tens place of a two digit number is three times the digit at the units place. If the digits
are reversed, the new number will be 36 less than the original number. Find the number.

Answer 1

Question:

The digit at the tens place of a two digit number is three times the digit at the units place. If the digits

are reversed, the new number will be 36 less than the original number. Find the number.

To find:

★ To find the number .

Answer:

$The \: number \: is \: \underline{ \: \underline{\:\sf\pink{62}\:}\:}.$

Step-by-step explanation:

The digit at the tens place of a two digit number is three times the digit at the units place.

Now Assuming the values ,

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

$\therefore$ The number is $\underline{\bold{10x+y}}$

Also given, $x = 3y \: --->(1)$

Reversed number will be $\underline{\bold{10y+x}}$

The new number will be 36 less than the original number.

$\implies (10x + y) - (10y + x) = 36$

Now substituting the value of x.

$\implies \big[10(3y) + y\big] - \big[ 10y + 3y\big] = 36$

$\implies 30y + y - 10y - 3y = 36$

$\implies 18y = 36$

$\implies \boxed{y = 2}$

Now substituting the value of y in eq (1)

$\hookrightarrow x = 3(2)$

$\hookrightarrow \boxed{x = 6}$

The values of x, y are 6 and 2 respectively.

$\longmapsto The \: number = 10x+y$

$\longmapsto 10(6)+2$

$\longmapsto \boxed{62}$

$\therefore The \: number \: is \: \underline\bold{62}.$

Test yourself :

1. A number consists of two digit whose sum is 9.If 9 is subtracted from the number the digits interchange their places. Find the number.

2. A number consists of two digit of which ten's digit exceeds the units digit by 6. The number itself is equal to ten times the sum of its digits. Find the number.