Question

Consider a three-digit number with the following properties:
I. If its digits in units place and tens place are interchanged, the number increases by 36,
II. If its digits in units place and hundreds place are interchanged, the number decreases by 198. Now suppose that the digits in tens place and hundreds place are interchanged. Then the number.
A. increases by 180
B. decreases by 270
C. increases by 360
D. decreases by 540

Answer 1

Correct Answer - D
Let Three digit No is 100 a + 10 b + c
Given 100 a + 10 b + c =100 a + 10 c + b-36
9b-9c+36=0
c=b+4
b=c-4
Also given 100 a + 10 b +c = 100c+ 10 b + a + 198
99 a - 99 c = 198
a = c + 2
`therefore` Now 100 a + 10 b + c - (100 b+ 10 a + c)
`=90 (a-b)`
`= 90 (c+2-c+4) " "(use (i) & (ii))`
=540
`therefore` value decreases by 540