Question

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2. A two digit number is equal to 7 times the sum of its digits. The number formed by
reversing its digits is less than the original number by 18. Find the original number.
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Answer 1

Answer:

Your answer is 42

Step-by-step explanation:

let the two-digit number be 10x+y

given,the number is 7 times the sum of its digits

⇒10x+y=7(x+y)

10x+y=7x+7y

3x=6y

x=2y

the number formed by reversing the digits is 18 less than original number

⇒10x+y-(10y+x)=18

  10x+y-10y-x=18

  9x-9y=18

 9(x-y)=18

 (x-y)=18/9=2

⇒x-y=2

x=2y

⇒2y-y=2

y=2

x=4

∴the number is 42

Answer 2

Answer:

42

Step-by-step explanation:

Let the digits in ones place be x and ten’s place be y The original number = 10y + x Number formed by interchanging the digits = 10x + y Given (10y + x) = 7(x + y) Þ 10y + x = 7x + 7y Þ 7x + 7y – x – 10y = 0 Þ 6x – 3y = 0 Þ 2x – y = 0 → (1) It is also given that on reversing the digits the number obtained is 18 less than the original number Hence 10x + y = (10y + x) – 18 Þ 10x + y – 10y – x = – 18 Þ 9x – 9y = – 18 Þ x – y = – 2 → (2) Subtract (2) from (1) 2x – y = 0 x – y = – 2 ------------- x = 2 Put x = 2 in 2x – y = 0 2(2) – y = 0 ∴ y = 4 Therefore the original number is 42.