Question

Sum of the digits of a two digit number is 7. When we interchange the digits, it is found that the resulting new number is greater than the original number by 45. What is the two digit number? ​

Answer 1

Answer:

When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two- digit ...

Answer 2

➢Given :

• Sum of the the digits of a two digit number is 7.

• When we interchange the digits, it is found that the resulting new number is greater than the original number by 45.

➢To find :

• What is the original number.

➢Solution :

• Let us consider the two digits be x and y.

• Therefore, the two digit number is 10x + y.

➢According to the question :

$x + y = 7 \: \: (1)$

$10y + x = 10x + y + 45 \\ 10y - y - x = 10x = 45 \\ 9y - 9x = 45 \\ y - x = 5 \: (2)$

• Add ( 1 ) and ( 2 )

$x + y + y - x = 7 + 5 \\ 2y = 12 \\ y = 16$

➢Putting the value of y in 1

$x + 6 = 7 \\ x = 7 - 6 \\ x = 1$

• Thus, the required number is :-

$10 \times 1 + 6 \\ = 16$

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