Sum of arithmatic and algebra

Algebra Level 2

We have a two digit number AB the digits of this number is alternated to form another number BA if the value of A+B=9 find out the value of AB+BA

Note:- Here AB means a two digit number having A at ten's place and B at one's place not multiplication of A with B.


The answer is 99.

Aman Sharma by Aman Sharma , 25, India

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2 solutions

Azadali Jivani
Jul 27, 2015

18+81=99
27+72=99
36+36=99
45+54=99


Note: 1+8=9 & 8+1=9 and so on

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Harnish Makkar
Aug 14, 2014

Let's say AB is 45, then BA is 54 (5+4 = 9) 45 + 54 = 99

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What if AB=63 and BA=36 in this case 3+6=9 also how you guessed that AB is surely 45 can you please explain

Aman Sharma - 6 years, 10 months ago

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I just guessed. However 63 + 36 = 99 also works So does 18 and 81 27 and 72 36 and 63 45 and 54 and vice versa

Harnish Makkar - 6 years, 10 months ago

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Ohhh and i thought you used some algebric techniq to solve it

Anyway nice solution

Aman Sharma - 6 years, 10 months ago

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@Aman Sharma – Is there any technique .If yes ,please post it...

Archiet Dev - 6 years, 9 months ago

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@Archiet Dev – Here is the actual solution:- Since AB is a two digit number so having B at one 's place and A at ten's place so:- A B = 10 A + B AB=10A+B now after alternating the digits we get number BA :- B A = 10 B + A BA=10B+A adding the equations:- A B + B A = 11 ( A + B ) AB+BA=11(A+B) accourding to question:-A+B=9 so:- A B + B A = 11 × 9 = 99 AB+BA=11×9=99

Aman Sharma - 6 years, 9 months ago

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