Question

Find the sum of the digits of the largest even three digit number which is not changed when its units and hundreds digits are interchanged ?
(a) 22 (b) 23 (c) 24 (d) 25
please if possible solve on paper

Answer 1

Step-by-step explanation:

MATHS

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

B .

Decreases by 270

C .

Increases by 360

D .

Decreases by 540

October 15, 2019Farhaz Edge

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VIDEO EXPLANATION



ANSWER

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+36⇒c−b=4…eqn(1)

Now, Interchanging units and hundreds places digits, we get

⇒100c+10b+a=100a+10b+c−198⇒a−c=12…eqn(2)

From equation 1 and 2,

a−b=6…eqn(3)

Suppose number is increased by x, If we change tens and hundreds digits, 

⇒100b+10a+c=100a+10b+c+x⇒−x=90a−90b⇒x=−540

Thus, number is decreased by 540.

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