Math, asked by princedixit1296, 11 months ago

A certain number between 10 and 100 is 8 time the sum of its digit and if 45 subtracted from it the digit will be reversed.find the number.​

Answers

Answered by jinadevkv
4

Answer:

72

Step-by-step explanation:

(7+2)*8 = 9*8 = 72

72 - 45 = 27

Answered by ItzEnchantedGirl
14

Answer:

Answer:

Given :-

A certain number between 10 and 100 is 8 times the sum of its digits, and if 45 be subtracted from it, the digits will be reversed.

To Find :-

What is the number.

Solution :-

Let,

\mapsto Digits at unit's place = x

\mapsto Digits at ten's place = y

Then, the original number will be :

\leadsto \sf\bold{\pink{10x + y}}

According to the question,

\implies \sf 10x + y =\: 8(x + y)

\implies \sf 10x + y =\: 8x + 8y

\implies \sf 10x - 8x =\: 8y - y

\implies \sf 2x =\: 7y

\implies \sf\bold{\purple{x =\: \dfrac{7y}{2}\: ------\: (Equation\: No\: 1)}}\\

Again,

\implies \sf 10x + y - 45 =\: 10y + x

\implies \sf 10x + y - 45 - 10y - x =\: 0

\implies \sf 10x - x + y - 10y - 45 =\: 0

\implies \sf 9x - 9y - 45 =\: 0

\implies \sf 9(x - y - 5) =\: 0

\implies \sf (x - y - 5) =\: 0 \times 9

\implies \sf\bold{\purple{x - y - 5 =\: 0\: ------\: (Equation\: No\: 2)}}\\

Now, by putting the value of x in the equation no 2 we get,

\implies \sf \dfrac{7y}{2} - y - 5 =\: 0

\implies \sf \dfrac{7y - 2y - 10}{2} =\: 0

By doing cross multiplication we get,

\implies \sf 7y - 2y - 10 =\: 2(0)

\implies \sf 7y - 2y - 10 =\: 0

\implies \sf 7y - 2y =\: 10

\implies \sf 5y =\: 10

\implies \sf y =\: \dfrac{\cancel{10}}{\cancel{5}}

\implies \sf \bold{\green{y =\: 2}}

Now, by putting the value of y in the equation no 2 we get,

\implies \sf x - y - 5 =\: 0

\implies \sf x - 2 - 5 =\: 0

\implies \sf x - 7 =\: 0

\implies \sf\bold{\green{x =\: 7}}

Hence, the required original number is :

\longrightarrow \sf Original\: number =\: 10x + y

\longrightarrow \sf Original\: number =\: 10(7) + 2

\longrightarrow \sf Original\: number =\: 70 + 2

\longrightarrow \sf\bold{\red{Original\: number =\: 72}}

\therefore The original number is 72.

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