Question

Liner equation

the sum of the digits of a two digit number is 7 . the number obtained by interchangeing the digits exceeds the original number by 27 find the number .​

Answer 1

Answer:

The answer of this question can be checked by interchanging the digits and then using the interchanged number in Equation (3) and checking for the value. Interchanged number is 52. So y is 5 and x is 2. Hence, the calculated answer is correct.

Step-by-step explanation:

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Answer 2

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:

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