Question

A two digit number is 7 times the sum of its digits . The number formed by reversing the digits is 18 less than original number . The number is

Answer 1

Answer:

the original number = 42

Step-by-step explanation:

given that,

A two digit number is 7 times the sum of its digits .

let the digits be x and y

so,

number = 10y + x

According to the question

10y + x = 7(x +y)

10y + x = 7x + 7y

10y - 7y + x - 7x = 0

3y - 6x = 0

3(y - 2x) = 0

y - 2x = 0

y = 2x.... (1)

also,

given that,

The number formed by reversing the digits is 18 less than original number

so,

number formed by reversing the digits = 10x + y

so,

10x + y = 10y + x - 18

10x - x + y - 10y = -18

9x - 9y = -18

9(x - y) = -18

x - y = -18/9

x - y = -2 .....(2)

putting the value of y on (2)

x - y = -2

x - 2x = -2

-x = -2

x = 2

from (1)

y = 2x

y = 2(2)

y = 4

x = 2

number

= 10y + x

= 10(4) + 2

= 40 + 2

= 42

so,

the original number = 42

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VERIFICATION

1.) two digit number is 7 times the sum of its digits

two digit number = 42

digits = 4 and 2

42 = 7(4 + 2)

42 = 7×6

42 = 42

__________

2.) The number formed by reversing the digits is 18 less than original number .

reversed number = 24

original number = 42

42 = 24 + 18

42 = 42

___________

Answer 2

Answer:

The required number is 42.

Step-by-step explanation:

Given Problem:

A two digit number is 7 times the sum of its digits . The number formed by reversing the digits is 18 less than original number . The number is?

Solution:

To Find:

The required number.

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Method:

Let tenth digit is a and unit digit is b

So,

The number is ‘ab’ and value is 10a+b

Now,

Sum of two digit is a+b

$\implies\7 (a+b) =10a+b or 7a+7b=10a+b , or \:6b=3a, a=2b$

Now,

Reversing the digit value is 10b+a

$10b+a+18=10a+b , or 9b+ 18 = 9a =18b, or\:9b=18$

Or,

b=2 and a=2b=4

Hence,

The required number is 42.