Question

Topic - Linear Equations

The sum of the digits of a two-digit number is 7. If 2 is subtracted from the number formed by interchanging the digits, the result is double the original number. Find the original number.

​

Answer 1

Step-by-step explanation:

Given :-

The sum of the digits of a two-digit number is 7. If 2 is subtracted from the number formed by interchanging the digits, the result is double the original number.

To find :-

Find the original number. ?

Solution :-

Let the digit at tens place in the two digit number be X

The place value of X = 10×X = 10X

Let the digit at ones place be Y

The place value of Y = 1×Y = Y

The original number = 10X+Y

The number obtained by reversing the digits = 10Y+X

Given that

The sum of the digits in the number = 7

=> X+Y = 7

=> X = 7-Y -------------(1)

And

If 2 is subtracted from the number formed by interchanging the digits, the result is double the original number.

=> 10Y+X -2 = 2(10X+Y)

=> 10Y+X-2 = 20X+2Y

=> 10Y+X-2-20X-2Y = 0

=> 8Y-19X-2 = 0

=> 8Y-19(7-Y)-2 = 0 (From (1))

=> 8Y-133+19Y-2 = 0

=> 27Y-135 = 0

=> 27Y = 135

=> Y = 135/27

=> Y = 5

On Substituting the value of Y in (1) then

=> X = 7-5

=> X = 2

Therefore the number = 25

Answer:-

The original number for the given problem is 25

Used formulae:-

The original number = 25

Sum of the digits = 2+5 = 7

The number obtained by reversing the digits = 52

On subtracting 2 from 52 then

=> 52-2

=> 50

=> 2×25

=> Double tha original number

Verified the given relations in the given problem.

Answer 2

25

Step-by-step explanation:

QUESTION :-

The sum of the digits of a two-digit number is 7. If 2 is subtracted from the number formed by interchanging the digits, the result is double the original number. Find the original number.

_________________________

SOLUTION :-

Let,

The digit at tens place be x

and the digit at ones place be y

So,

Original number = 10x + y

And,

Number formed by interchanging the digits = 10y + x

_______________________

Sum of two digit of number = 7

=> x + y = 7

=> x = 7 - y....(1)

and,

2 subtracted by Number formed by interchanging digit = doubles the original number

=> (10y + x) - 2 = 2(10x + y)

=> 10y + x - 2 = 20x + 2y

=> -2 = 20x - x + 2y - 10y

=> 19x - 8y = - 2

By putting the value of x by (1) , we get,

=> 19(7 - y) - 8y = - 2

=> 133 - 19y - 8y = - 2

=> -27y = -2-133

=> -27y = - 135

=> y = (-135) ÷ (-27)

=> y = 5

Now,

put the value of y in (1),

x = 7 - y

=> x = 7-5

=> x = 2

So,

The original number = 10x + y

= 10(2) + 5

= 20 + 5

= 25

_______________________

Hence, The original number is 25.

And,

when 2 subtracted by Number formed by interchanging digit (52) = 2×number(25)

_______________________

Hope it helps.

#BeBrainly :-)