Question

Sum of the digits of a two digit no. is 9 .The number obtained by interchanging the digits is 18 more than twice the original number.the original no. is .
a)72
B)27
C)36
d)63
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Answer 1

Answer:

Let the unit digit be X.

Then the tense digit be(X+18)

Original number = 10×tense digit+ unit digit

= 10(X+18) + X

= 10X+180 + X

= 11X+180

After interchanging

Unit digit be (X+18)

Tense digit be X

New number = 10×tense digit+unit digit

= 10×X+X+18

= 11X+18

A/Q 11X+180 = 11X+18

or 22X=198

therefore X = 198/22

Unit digit = X = 9

Tense digit = 9+18

so, number = 27

Answer 2

Answer:

(B) 27

Step-by-step explanation:

Define the 2-digit number:

Let the digit in the ones place = x

Let the digit in the tens place = y

The two digit number is (10y + x)

Form the first equation:

Sum of the digits is 9

⇒ x + y = 9

⇒ x = 9 - y

Form the second equation:

The number obtained by interchanging the digit is 18 more than twice the original number.

⇒  (10x + y) = 2(10y + x) + 18

⇒ 10x + y = 20y + 2x + 18

⇒ 19y - 8x + 18 = 0

Substitute first equation into the second equation:

19y - 8(9 - y) + 18 = 0

19y - 72 + 8y + 18 = 0

27y - 54 = 0

27y = 54

y = 2

Substitute y = 2 into first equation:

x = 9 - 2

x = 7

Find the number:

Original number = 10y + x

Original number = 10(2) + 7

Original number = 27

Answer: The original number is 27.