Question

The sum of the digit of a two digit number is 7. If the digit are reversed the nee number decreased by 2 ,equal twice the original number .find
the number
​

Answer 1

Answer:

25

Explanation:

Let one digit  be x  and other one be 7-x so the digit is=10(7-x)+x

70-9x

now by reversing the digit

the digit is 9x+7

by decreasing 2 in new one

(9x+5)=2(70-9x)

27x=135

x=5

(7-5)10

Answer 2

${\large{\underline{\underline{\boxed{\boxed{\mathfrak{\red{AnsWer:}}}}}}}}$

• Two digit number = 25.

${\large{\underline{\underline{\boxed{\boxed{\mathfrak{\red{Step\:By\:Step\:Explanation:}}}}}}}}$

${\star{\underline{\red{\bf{Given:}}}}}$

• Sum of digit of two digit number is 7.
• If digit is reversed the number is decreased by 2 and equal to twice of original number.

${\star{\underline{\blue{\bf{To\:Find:}}}}}$

• The Number.

${\star{\underline{\pink{\bf{Solution:}}}}}$

Let two digits are x and y.According to question,

$\implies$ x + y = 7

$\implies$ y = 7 - x ......(1)

Now, it given that if digit is reversed the number is decreased by 2 and equal to the twice of original number.

$\implies$ 10y + x - 2 = 2(10x + y)

$\implies$ 10y + x - 2 = 20x + 2y

$\implies$ 10y - 2y = 20x - x + 2

$\implies$ 8y = 19x + 2

$\implies$ 19x + 2 - 8y = 0

$\implies$ 19x + 2 - 8(7 - x) = 0

$\implies$ 19x + 2 - 56 + 8x = 0

$\implies$ 27x - 54 = 0

$\implies$ 27x = 54

$\implies$ $\sf{x =\dfrac{54}{27}}$

$\implies$ x = 2

Hence, x = 2

So, y = 7 - x

$\implies$ y = 7 - 2

$\implies$ y = 5

Hence, Two digit number = 25.

${\star{\underline{\green{\bf{Verification:}}}}}$

$\implies$ Sum of digit of two digit number = 7

$\implies$ x + y = 7

$\implies$ 2 + 5 = 7

Hence Proved!!!