Question

18. One of the two digit
number is four times the
other digit. If you
interchange the digits of
this two digit number and
add the resulting number
to the original number you
get 55. What is the original
number? ЗМ​

Answer 1

Answer:

Step-by-step explanation:

let the digit in ones place be x

let the digit in tens place be 4 = 4x

the digits are - 40x,x

40x + x + 10x +4x =55

55x = 55

x = 55/55 =1

therefore , x=1

the orginal number is: 4x = 4, x = 1, so the number is 41

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Answer 2

Original Number = 41

Step-by-step explanation:

Given:

• One of the two digit number is 4 times the other digit.
• After interchanging digits and adding resulting number with original we get 55.

To Find:

• What is the original number ?

Solution: Let the tens and ones digit of original number be x and y respectively. Therefore original number is 10x + y

One digit = 4 times of other

x = 4y........(1)

[ Now interchanging the digits of number new number formed will be ]

• Reversed number = 10y + x

A/q

• After interchanging digits and adding resulting number with original we get 55.

$\implies{\rm }$ 10y + x + 10x + y = 55

$\implies{\rm }$ 11y + 11x = 55

$\implies{\rm }$ 11(y + x) = 55

$\implies{\rm }$ y + x = 55/11

$\implies{\rm }$ y + 4y = 5

$\implies{\rm }$ 5y = 5

$\implies{\rm }$ y = 5/5

$\implies{\rm }$ y = 1

So the digits of number are

• Ones digit is y = 1

• Tens digit is x = 4y = 4 × 1 = 4

Hence the original number is 10x + y

= 10(4) + 1

= 41