Question

A 3 digit number is equal to 17 times of sum of its digit. If 198 added to the number, digit are interchange. The addition of first and third digit is 1 less than middle. find the number... If anyone solve it by step by step I mark as brainliest... ​

Answer 1

$\bf{\underline{Question:-}}$

• A 3 digit number is equal to 17 times of sum of its digit. If 198 added to the number, digit are interchange. The addition of first and third digit is 1 less than middle. find the number.

$\bf{\underline{Solution:-}}$

Let

• the three-digit number be xyz.
• its numerical value = 100x + 10y + z

• According to first information provided in the question,

⏩ 100x + 10y + z = 17(x + y + 2)

⏩ 100x + 10y +z = 17x + 17y +172

⏩ 83x - 7y- 16z =0 ----equ(¡)

• Number obtained by reversing the digits: zyx

• its numerical value = 100z + 10y + X

• According to second Information provided in the question,

⏩ (100x + 10y + 2) + 198 = 100z + 10y +x

⏩ 99z - 99x = 198

⏩ z - x = 198/99

⏩ z -x = 2

• ⏩ z = x + 2 ----equ(¡¡)
• According to third Information provided in the question,

⏩ x + z = -1

⏩ x + x +2 = y - 1 【from equ(¡¡)】

⏩ y = 2x + 3 Substituting z and y in (¡),

⏩ 83x - 7(2x +3) – 16(x + 2)=0

⏩ 83x - 14x + 21- 16x - 32 = 0

⏩ 53x -53 =0

⏩ 53x =53

⏩ x = 53/53

• ⏩ x = 1

⏩ y=2x + 3 = 2(1) + 3

⏩ y =2+3

⏩ y = 5

⏩ z = x + 2 =

⏩ z = 1 +2

• ⏩ z = 3

$\bf{\underline{Hence:-}}$

• the three-digit number is 153.

__________________________

Answer 2

Step-by-step explanation:

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Asked on October 15, 2019 by

Mani Jgn

A three digit number is equal to 17 times the sum of its digits. If 198 is added to the number, the digits are interchanged The addition of first and third digit is 1 less than middle digit. Find the number

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VIDEO EXPLANATION

ANSWER

Let the number be abc

So number is 100a+10b+c

⇒100a+10b+c=17(a+b+c)

⇒83a=7b+16c .......(i)

198+100a+10b+c=a+10b+100c

Or 198+99a=99c

Hence c−a=2⇒c=a+2 .....(ii)

Also, given a+c=b−1

Now as a+c=b−1 and c=a+2

⇒a+a+2=b−1

⇒b=2a+3

now in eq(i)

substitute the values of b and c

83a=7b+16c

⇒83a=7(2a+3)+16(a+2)

⇒53a=21+32

⇒a=1

⇒c=a+2=3

⇒b=2a+3=5

So the number is 153