Question

the ratio of two digit natural number to a number formed by reversing its digit is 4:7. which of the following is the sum of all the numbers of all such pairs
1-99
2-198
3-330
4-32

Answer 1

glad traffic Kno if it doesn't happen to me that would be in with with

Answer 2

Answer:

330

Step-by-step explanation:

Let the two digit number be 10 a + b

When the digits are reversed

Reversed Number = 10b+a

Now we are given that the ratio of two digit natural number to a number formed by reversing its digit is 4:7.

So,$\frac{10a+b}{10b+a}=\frac{4}{7}$

$7(10a+b)=4(10b+a)$

$70a+7b=40b+4a$

$66a=33b$

$\frac{a}{b}=\frac{33}{66}$

$\frac{a}{b}=\frac{1}{2}$

So, let us list down all possible values for a and b.

a =1 so , b = $2a = 2 \times 1 = 2$

So, number = 12 and reversed number 21

a =2 so , b = $2a = 2 \times 2= 4$

So, number = 24 and reversed number 42

a =3 so , b = $2a = 2 \times 3 = 6$

So, number = 36 and reversed number 63

a =4 so , b = $2a = 2 \times 4 = 8$

So, number = 48 and reversed number 84

The sum of all the numbers:

12 + 21 + 24 + 42 + 36 + 63 + 48 + 84 = 330.

Hence he sum of all the numbers of all such pairs  is 330.