Math, asked by mahikoka17, 11 hours ago

The sum of a two digit number and the number formed by interchanging its digits is 110.if 10 is subtracted from the first number,the new number is 4 more than 5 times the sum of the digits in the first number .find the first number.​

Answers

Answered by Dalfon
43

Answer:

64

Step-by-step explanation:

Let's say the ones digit number be x and tens digit number be y.

So, the original number is 10y + x and interchanged number is 10x + y.

The sum of a two digit number and the number formed by interchanging its digits is 110.

As per given statement,

→ 10y + x + 10x + y = 110

→ 11x + 11y = 110

→ x + y = 10

→ x = 10 - y

Also, said that if 10 is subtracted from the first number

→ 10y + x - 10

The new number is 4 more than 5 time the sum of its digits in the first number.

→ 4 + 5(x + y)

Therefore,

→ 10y + x - 10 = 4 + 5(x + y)

→ 10y - 5y + x = 4 + 10 + 5x

→ 5y = 14 + 4x

Substitute value of x above

→ 5y = 14 + 4(10 - y)

→ 5y = 14 + 40 - 4y

→ 5y + 4y = 54

→ 9y = 54

→ y = 6

Substitute value of y in x

→ x = 10 - 6

→ x = 4

Therefore, the first number = 10y + x = 10(6) + 4 = 64

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