Question

13) A number consists of two-digits. The digit at the units place is 3 times the digit
at the tens place. If 36 is added to the number, the digits are reversed. Find the number
​

Answer 1

original number

tens digit = x then ones digit = 3x

value of 10s digit = 10x 

value of 1s digit = 3x

number = 10x + 3x = 13x

reversed number

10s digit = 3x and 1s digit = x

value of 10s digit = 30x

value of 1s digit = x

number = 30x + x = 31x

relation between original and reversed number

original number + 36 = reversed number

13x + 36 = 31x

36 = 31x - 13x

36 = 18x

36/18 = x

x = 2

therefore;

original number = 13x = 13*2 = 26

reversed number = 62

Answer 2

GIVEN:

• The digit at the units place is 3 times the digit at the tens place
• If 36 is added to the number, the digits are reversed

TO FIND:

• What is the original number ?

SOLUTION:

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

❍ Number = 10x + y

CASE:- ❶

➣ The digit at the units place is 3 times the digit at the tens place

According to question:-

$\bf{\dashrightarrow y = 3x.... 1) }$

CASE:- ❷ 

➣ If 36 is added to the number, the digits are reversed

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

According to given conditions:-

◈ Original number + 36 = 10y + x

$\rm{\dashrightarrow 10x + y + 36 = 10y + x }$

$\rm{\dashrightarrow 10x + y -(10y+x) = -36 }$

$\rm{\dashrightarrow 10x +y-10y-x = -36}$

$\rm{\dashrightarrow 9x - 9y = -36 }$

Divide by '9' on both sides

$\rm{\dashrightarrow x - y = -4 }$

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

$\rm{\dashrightarrow x - 3x = -4 }$

$\rm{\dashrightarrow -2x = -4 }$

$\rm{\dashrightarrow x = \cancel\dfrac{-4}{-2} }$

$\bf{\dashrightarrow \star \: x = 2 \: \star }$

Put the value of 'x' in equation 1)

$\rm{\dashrightarrow y = 3 \times 2 }$

$\bf{\dashrightarrow \star \: y = 6 \: \star }$

❖ Number = 10x + y

➺ Number = 10(2) + 6

➺ Number = 20 + 6

✰ Number = 26 ✰

❝ Hence, the Number formed is 26 ❞

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