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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
Increased by 180
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B
Decreases by 270
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C
Increases by 360
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D
Decreases by 540
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Solution

The correct option is D Decreases by 540
Let a,b and c are the hundreds, tens and units places digits respectively. then digit =100a+10b+c
Interchanging units and tens places digits, we get
100a+10c+b=100a+10b+c+36cb=4eqn(1)
Now, Interchanging units and hundreds places digits, we get
100c+10b+a=100a+10b+c198ac=12eqn(2)
From equation 1 and 2,
ab=6eqn(3)
Suppose number is increased by x, If we change tens and hundreds digits,
100b+10a+c=100a+10b+c+xx=90a90bx=540
Thus, number is decreased by 540.

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