Question

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Answer 1

Given:-

• Sum of the digits of a two digit number = 7
• If the digits are interchanged, then the new number will exceed the original number by 27.
• Or in other words:
• New number - Original number = 27

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To find:-

• The two digit number.

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Solution:-

$\bigstar {\sf {\blue {Let\ the\ digit\ in\ units\ place\ be\ x.}}}$

$\bigstar {\sf {\blue {Let\ the\ digit\ in\ tens\ place\ be\ (7-x).}}}$

Original number = {10(7-x)}+x

$\implies \sf {70-10x+x}$

$\implies {\sf {\pink {70-9x}}}$

If we interchange the digits then,

$\bigstar {\sf {\green {The\ digit\ in\ units\ place\ is\ (7-x)}}}$

$\bigstar {\sf {\green {The\ digit\ in\ tens\ place\ is\ x.}}}$

Now,

New number = 10x + (7-x)

$\implies \sf {10x+7-x}$

$\implies {\sf {\red {9x+7}}}$

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A.T.Q:-

$\implies \sf {(9x+7) - (70-9x) = 27}$

$\implies \sf {9x+7 - 70+9x = 27}$

$\implies \sf {9x+9x+7-70 = 27}$

$\implies \sf {18x-63 = 27}$

$\implies \sf {18x = 27+63}$

$\implies \sf {x = \dfrac {90}{18}}$

$\implies {\bf {\orange {x = 5}}}$

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Original number:

Units digit = x

= 5

Tens digit = 7-x

= 7-5

= 2

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Final answer:-

$\boxed {\sf {\purple {The\ original\ number\ is\ 25.}}}$

Answer 2

☘️ Refer the attachment diagram.

$\Large\mathbb\pink{THANKS}$

$\Large\mathbb\green{HOPE\: IT'S\: HELPFUL}$