Math, asked by braunstrowman1, 1 year ago

A certain number of two digits is three times the sum of its digits and if 45 be added to it the digits will be reversed. Find the number ​

Answers

Answered by manjunpai2000
0

Answer:

Number is 27

Step-by-step explanation:

2+7 = 9

9×3 = 27

27+45 = 72

Answered by Anonymous
5

Originalnumber=27

\bigstar{\bold{original\:number=27}}

\bigstar{\bold{Reversed\:number=72}}

Step-by-step explanation:

\Large{\underline{\underline{\it{Given:}}}}

A number = 3 times the sum of the digits

If 45 is added to it, the digits are reversed

\Large{\underline{\underline{\it{To\:Find:}}}} </p><p>

The numbers

</p><p></p><p>\Large{\underline{\underline{\it{Solution:}}}} </p><p>

➦ Let us assume the unit's digit of the number as y

➦ Let us aasume the ten's digit of the number as x

➦ Hence,

The number = 10x + y

➦ By given

The number = 3 × sum of digits

10x + y = 3 (x + y)

10x + y = 3x + 3y

10x - 3x = 3y - y

7x = 2y

y = 7x/2 -----(1)

➦ Also by given,

The number + 45 = Reversed number

10x + y + 45 = 10y + x

10x - x + 45 = 10y - y

9x + 45 = 9y

➦ Divide the whole equation by 9

x + 5 = y

➦ Substitute the value of y from equation 1

x + 5 = 7x/2

2x + 10 = 7x

2x - 7x = -10

5x = 10

x = 10/5

x = 2

➦ Hence the ten's digit of the number is 2

➦ Substitute the value of x in equation 1

y = 7 × 2/2

y = 7

Hence the unit's digit of the number = 7

Therefore the original number is,

Original number = 10x + y

Original number = 10 × 2 + 7

Original number = 27

\boxed{\bold{Original\:number=27}}

➦ Now the reversed number is given by,

Reversed number = 10y + x

Reversed number = 10 × 7 + 2

Reversed number = 72

  \boxed{\bold{Reversed\:number=72}}

\Large{\underline{\underline{\it{Verification:}}}}

➦ Number = 3 × sum of the digits

27 = 3 × (2 + 7)

27 = 3 × 9

27 = 27

➦ Original Number + 45 = Reversed number

27 + 45 = 72

72 = 72

➦ Hence verified.

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