Question

4 The sum of the digits of a two digit number is 7. If the digits are reversed, the new
number increased by 3 equals 4 times the original number. Find the number.

Royan Raj bro help​

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 ,

 $\longrightarrow\sf x+y = 7 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .....................(1)$

According to the second condition ,

 $\longrightarrow\sf 4(10x+y)+3 = 10y+x \\\\\longrightarrow 40x+4y - 3 = 10y+x \\\\\longrightarrow 40-x+4y-10y = 3 \\\\\longrightarrow 39 x-6y =-3 \\\\\longrightarrow 13x-2y = 1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .................. ...(2)$

Equation (1) × 2

 $\longrightarrow\sf 2x+2y = 14 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .................. ...(3)$

Equation (2) + Equation (3)

 $\longrightarrow\sf 15x= 15\\\\\longrightarrow x = 1$

Substitute x = 1 in equation (1) ,

 $\longrightarrow \sf 1+y = 7 \\\\\longrightarrow y = 6$

Two digit number = 16

Answer 2

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