Question

when a two digit number is multiplied by 9, it becomes 2 times of the number that is obtained by interchanging the digits. if the difference of the digits is 7, find the number

Answer 1

let the units digit of the no. be x-7
and tens digit of no. be x
(As difference of 2 digits is 7)
so the 2 digit no. = 10(x-7)+x
It is multiplied by 9
=>9*(10(x-7)+x)

Twice the no. formed when digits are interchanged
which means tens digit becomes unit digit and vice versa.
=>2*(10x+(x-7))

Given that,

9*(10(x-7)+x) = 2*(10x+(x-7))
90(x-7) + 9x = 20x +2(x-7)
88(x-7) = 11x
88x - 616= 11x
77x = 616
tens digit =x= 8
unit digit= x-7= 1

The no. is 18


Verification:
1. Difference b/w units place and tens place= 7
2. 18*9= 2*81
=> 162 = 162
=> LHS = RHS

Data matched...

;)
Hope it helps
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