Question

6. The digit at the ten's place of a two digit number
is four times that in the unit's place. If the digits
are reversed, the new number will be 54 less than
the original number. Find the original number.
Check your solution.
7
Amber consists of weite​

Answer 1

SOLUTION :-

Let,

Digit in ten's place = x

Digit in one's place = y

Two digit number = 10x + y

According to the first condition,

$\longrightarrow\sf x = 4y \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ................(1)$

According to the second condition,

$\longrightarrow\sf 10x+y-54 = 10y+x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ................(2)$

Substitute the value of x in eq (2),

$\longrightarrow\sf 10(4y)+y-54= 10y+4y \\\\\longrightarrow 40y +y-54= 10y+4y \\\\\longrightarrow 41y-54 = 14y \\\\\longrightarrow 41y-14y = 54 \\\\\longrightarrow 27 y = 54 \\\\\longrightarrow \bf y = 2$

Digit in one's place = 2

Digit in ten's place = 2 × 4 = 8

Two digit number = 82

Answer 2

$\Large{\underline{\underline{\green{\sf Given:}}}}$

✥ Ten's place of a two digit number is 4times that in the unit's place.

✥ If digits are reversed the new number will be 54 less than the original number.

$\Large{\underline{\underline{\orange{\sf Find:}}}}$

✣ What is the original number

$\Large{\underline{\underline{\red{\sf Solution:}}}}$

Let, 1st digit of a two digit number be x

and 2nd digit be y

$\sf \therefore 2digit \: no. \: is \: 10x + y$

Now,

$\red{\mathbb{ACCORDING \: TO \: QUESTION}}$

⎇ $\sf x = 4y.....(1)$

When, digit is reversed the new number = 10y + x

Hence,

⎇ $\sf 10y + x = 10x + y - 54.....(2)$

Taking eq(2)

$\sf \to 10y + x = 10x + y - 54$

$\sf \to x - 10x + 10y - y= - 54$

$\sf \to -9x + 9y= - 54$

$\sf \to -9(x - y)= - 54$

$\sf \to x - y= \cancel{\dfrac{ - 54}{ - 9} } = 6$

$\sf \to x - y=6$

Using value of x = 4y we, get

$\sf \to x - y=6$

$\sf \to 4y - y=6$

$\sf \to 3y=6$

$\sf \to y= \cancel{ \dfrac{6}{3} } = 2$

$\sf \to y=2$

Use this value of y in eq(1) we, get

➵ $\sf x = 4y$

➵ $\sf x = 4(2)$

➵ $\sf x = 8$

➵ $\sf So, x = 8$

____________________

$\underline{\underline{\scriptsize{\sf\therefore original \: no. = 10x + y = 10(8) + 2 = 80 + 2 = 82}}}$