Question

The tens digit of a number is four times it's ones digit . If 27 is subtracted from the number digits of the difference obtained are reverse of those of number. Find the number.

Answer 1

GIVEN:

• The tens digit of a number is four times it's ones digit.
• If 27 is subtracted from the number digits of the difference obtained are reverse of those of number.

TO FIND:

• What is the number ?

SOLUTION:

Let the digit at unit's place be 'y' and the digit at ten's place be 'x'

❍ NUMBER = 10x + y

CASE:- 1

The tens digit of a number is four times it's ones digit.

According to question:-

$\bf{\hookrightarrow x = 4y....1) }$

CASE:- 2

If 27 is subtracted from the number digits of the difference obtained are reverse of those of number.

 ❒ Number obtained by reversing the digits = 10y + x

 ❒ Original number – 27 = Number obtained by reversing the digits

According to question:-

$\rm{\hookrightarrow 10x + y - 27 = 10y + x }$

$\rm{\hookrightarrow 10x + y - 10y - x = 27 }$

$\rm{\hookrightarrow 9x - 9y = 27 }$

Divide by 9 on both sides

$\bf{\hookrightarrow x - y = 3....2) }$

Put the value of 'x' from equation 1) in equation 2)

$\rm{\hookrightarrow 4y - y = 3 }$

$\rm{\hookrightarrow 3y = 3 }$

$\rm{\hookrightarrow y = \cancel\dfrac{3}{3} }$

$\bf{\hookrightarrow y = 1 }$

Put the value of 'y' in equation 1)

$\rm{\hookrightarrow x = 4 \times 1}$

$\bf{\hookrightarrow x = 4}$

• Number = 10x + y
• Number = 10(4) + 1
• Number = 40 + 1
• Number = 41

❝ Hence, the number formed is 41 ❞

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