M4maths Previous Puzzles

17 Jan 2019 Number

A number consists of 3 digits whose sum is 10. The middle digit is equal to the difference of the other two and the number will be increased by 99 if its digits are reversed. The square of the number is:

OPtion

1) 164036
2) 168100
3) 180625
4) 172225
5) 264196
6) 254016
7) 164025
8) 180616
9) 179776
10) None of these

Solution

let the digits of the No. be x. y & z
Hence, x+y+z=10.................(1)
z-x=y..............(2)

AS per the condition
(100z+10y+x)-(100x+10y+z)=99
=> z-x=1 -----(3)

Form (2) and (3), we deduce y=1

From equation (1) and (2)
we get,
x+z=9 and
z-x =1

Solving we get z= 5 and x = 4

So the number is 415 and its square is = 172225

Correct Option: 4 Best Solution (0)