Question

(b) The sum of a two-digit number and the number obtained after the digits are reversed, is 121.
If the difference of the digits is 3, find the number.​

Answer 1

Here is your

Answer

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Answer 2

$\huge \bf \underline \red{Answer}$

$\rm{ \boxed{ \underline{ \blue{ \rm{47 \: or \: 74 \: }}}}}$

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$\sf \huge \underline{➷ Question}$

The sum of a two-digit number and the number obtained after the digits are reversed, is 121. If the difference of the digits is 3, find the number.

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$\sf \underline{➷step \: by \: step \: explanation}$

let

• unit place be x

• ten's place be y

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then

• number will be 10y+x

• given from the question that obtained after the digits are reversed digits will be 10x+y

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$\sf \underline{➷from \: the \: question}$

$\tt \red{☆ \: (10y + x) + (10x + y) = 121}$

$\tt \blue{☆ \: x + y = 11}$

or

$\tt \green{☆ \: x - y = \ \frac{ + }{}3 }$

Now,

$\bold \pink{ \implies \: x + y = 11 \: is \: eq(1)}$

$\bold \pink{ \implies \: x - y = 3 \: is \: eq(2)}$

$\rm \underline{ \implies \: now \: adding \: eq(1)and(2) \: we \: get}$

$\bf \orange{ \implies \: 2x = 14 \: or \: x = 7}$

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• now we have to use to x=7 in equation one(1) we get

$\sf \purple{ \implies \: 7 + y = 11}$

$\sf \red{ \implies \: y = 11 - 7 = 4}$

$\bf{ \boxed{ \underline \blue{ \tt{so \: number \: is \: 47 \: }}}}$

Now,

$\rm \orange{ \implies \: x + y = 11.....is \: eq(3)}$

$\rm \orange{ \implies \: x - y = - 3 \: .......is \: eq(4)}$

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$\bf \underline{ \implies \: now \: adding \: eq(3) \: and \: (4) \: we \: get}$

$\tt \blue{ \implies2x = 8}$

$\tt \blue{ \implies \: x = 4}$

• now we have to use x=4 in equation (4) we get

$\tt \pink{ \implies \: y = 11 - 4 = 7}$

$\bf{ \boxed{ \underline \red{ \tt{ \: so \: number \: is \: 74 \: }}}}$

hence,

$\bf{\boxed{ \underline{ \tt{ \: red{ \: number \: is \: 47 \: or \: 74 \: }}}}}$

I hope it's help uh