Question

a is formed by reversing the digits of B.B is 45 less than A. the sum of the digits of B is 9 what is A​

Answer 1

A number B is formed by reversing the two digit number A. What are the digits of A?

(1) Difference of A and B lies between 70 and 80

(2) B is a two digit number

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Dec 20, 2010

surendar26 wrote:

A number 'b' is formed by reversing the 2-digit number 'a'.What are the digits of 'a' ?

1. Diff. of a and b lies b/w 70 and 80.

2. 'b' is a two digit number.

A number B is formed by reversing the two digit number A. What are the digits of A?

Every 2-digit number can be expressed as , where will be the tens digit (so between 1 and 9, note it can not be zero as in this case number won't be 2-digt anymore) and will be the units digit (so between 0 and 9).

Given: and .

(1) Difference of A and B lies between 70 and 80 --> --> --> there is only one multiple of 9 in this range - 72, so --> --> either and or and , so either or . Not sufficient.

(2) B is a two digit number --> just tells that . Not sufficient.

(1)+(2) As then and , so . Sufficient.

Answer 2

The value of A is 72.

Step-by-step explanation:

Since we have given that

Since the sum of the digits of B = 9

Let one's digit be 'x'

Let ten's digit be '9-x'

So, original number B = $10(9-x)+x=90-10x+x=90-9x$

Let the one's digit of A be 9-x

Let the ten's digit of A be x

So, A = $10x+9-x=9x+9$

According to question, it becomes,

$A-B=45\\\\9x+9-(90-9x)=45\\\\9x+9-90+9x=45\\\\18x-81=45\\\\18x=45+81\\18x=126\\\\x=\dfrac{126}{18}=7$

A would be $9x+9=9\times 7+9=63+9=72$

Hence, the value of A is 72.

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