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If the sum of the digits of a two digit number is 9 and the difference between the number and that formed by reversing the digits is 45 then

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If the sum of the digits of a two digit number is 9 and the difference between the number and that formed by reversing the digits is 45 then

Question

If the sum of the digits of a two digit number is 9 and the difference between the number and that formed by reversing the digits is 45 then number is A.81 B.72 C.45 D.54

## Answers ( )

GIVEN:TOFIND:SOLUTION:Let the digit at unit’s place beand the digit at ten’s place be

‘y’‘x’CASE:–1)✧

Sum of the digits of a two digit number is 9.Accordingtoquestion:–➸➸x=9–y....❶CASE:- 2)✧

Difference between the number and that formed by reversing the digits is 45.✦ReversedNumber=10y+x✦OriginalNumber–ReversedNumber=45Accordingtoquestion:–➸➸➸Taking commonfrom both sides

9➸x–y=5....❷Put the value ofin equation 2)

‘x’➸➸➸➸➸❮y=2❯Put the value ofin equation 1)

‘y’➸❮x=7❯◉

NUMBER=10x+y◉

NUMBER=10(7)+2◉

NUMBER=70+2◉

NUMBER=72❝72❞______________________Question:–If the sum of the digits of a two digit number is 9 and the difference between the number and that formed by reversing the digits is 45 then number is

A) 81

B) 72

C) 45

D) 54

Answer:–Originalnumber:–Let the digit in unit’s place be x

Then the digit in ten’s place will be (9 – x) [As the sum of digit is 9]

Hence, the number is 10(9 – x) + x = 90 – 9x

Newreversednumber:-Digit in unit’s place will be (9 – x)

Digit in ten’s place will be x

Hence, the number is 10x + (9 – x) = 9x + 9

We know that,Original number – new number = 45

=> 90 – 9x – (9x + 9) = 45

=> 90 – 9x – 9x – 9 = 45

=> -18x = -36

=> x = 2

Hence,original number = 90 – 9x = 90 – 18 = 72

Ans.Originalnumber=B)72