Banking Quantitative Aptitude Sample Paper Quantitative Aptitude Sample Paper-9

The sum of both digits of a two-digit number is 7. If the digits of the numbers are interchanged, the number so formed is greater than the original number by 27. Find the original number.                                        [NICL (AO) 2015]

A) 25

B) 26

C) 27

D) 28

E) 29

Correct Answer: A

Solution :

By going through option, we can eliminate the other 4.

\[\therefore \] 25 is the correct option, as sum of both digit is 7. and by interchanging the position of the digit i.e. 25 turns into 52.

Difference \[=52-25=27\]

Alternate Method

Let the digit at tens place be y and at one's place by x.

Then, according to; the question,

\[x+y=7\] ... (i)

and \[-\,(10y-x)+(10x+y)=27\]

\[\Rightarrow \] \[-\,9y+9x=27\]

\[-\,y+x=3\] ... (ii)

On solving Eqs. (i) and (ii), we get

\[2x=10\]\[\Rightarrow \]\[x=5\]

\[\therefore \] y = 2

So, number is 25.