# Sum of digits of a two-digit number is 9. When we interchange the digit it is found that the resulting new number is greater than the original number by 27. What is the two-digit number?

Answer

Verified

362.4k+ views

Hint: To solve the question, we form equations from the given information and solve those equations to unknow the value of digits of the two-digit number.

Complete step-by-step answer:

Let a, b be the tens and units digit of the two-digit number.

The given sum of the two digits of the two-digit number = 9

\[\Rightarrow \] a + b = 9 ………. (1)

The mathematical representation of the two-digit number with a, b at tens and units place respectively = 10a + b

Given that the digits at unit and tens place of two-digit number are reversed, the new two-digit number formed

= 10b + a

The new number formed exceeds the original number by the value 27.

\[\Rightarrow \] (10b + a) - (10a + b) = 27

9b - 9a = 27

9(b - a) = 27

b - a = 3 ………. (2)

By adding equations (1) and (2) we get

b - a + a + b = 9 + 3

2b = 12

\[\Rightarrow b=\dfrac{12}{2}=6\]

By substituting b value in equation (1) we get

a + 6 = 9

a = 9 – 6 = 3

Thus, the original number is equal to 10a + b

\[=\left( 10\times 3 \right)+6\]

= 30 + 6

= 36

\[\therefore \] The two-digit number is equal to 36.

Note: The possibility of mistake can be not using the mathematical representation of a two-digit number to ease the procedure of solving. The alternative procedure of solving can be using a hit-trial method for solving the equation, since a, b are digits of a number their values lie between 0, 9 and since a being the first digit of a two-digit number, it cannot be 0. Thus, we can try the other possible values and calculate the right answer.

Complete step-by-step answer:

Let a, b be the tens and units digit of the two-digit number.

The given sum of the two digits of the two-digit number = 9

\[\Rightarrow \] a + b = 9 ………. (1)

The mathematical representation of the two-digit number with a, b at tens and units place respectively = 10a + b

Given that the digits at unit and tens place of two-digit number are reversed, the new two-digit number formed

= 10b + a

The new number formed exceeds the original number by the value 27.

\[\Rightarrow \] (10b + a) - (10a + b) = 27

9b - 9a = 27

9(b - a) = 27

b - a = 3 ………. (2)

By adding equations (1) and (2) we get

b - a + a + b = 9 + 3

2b = 12

\[\Rightarrow b=\dfrac{12}{2}=6\]

By substituting b value in equation (1) we get

a + 6 = 9

a = 9 – 6 = 3

Thus, the original number is equal to 10a + b

\[=\left( 10\times 3 \right)+6\]

= 30 + 6

= 36

\[\therefore \] The two-digit number is equal to 36.

Note: The possibility of mistake can be not using the mathematical representation of a two-digit number to ease the procedure of solving. The alternative procedure of solving can be using a hit-trial method for solving the equation, since a, b are digits of a number their values lie between 0, 9 and since a being the first digit of a two-digit number, it cannot be 0. Thus, we can try the other possible values and calculate the right answer.

Last updated date: 28th Sep 2023

•

Total views: 362.4k

•

Views today: 8.62k

Recently Updated Pages

What do you mean by public facilities

Paragraph on Friendship

Slogan on Noise Pollution

Disadvantages of Advertising

Prepare a Pocket Guide on First Aid for your School

10 Slogans on Save the Tiger

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

What is meant by shramdaan AVoluntary contribution class 11 social science CBSE

The equation xxx + 2 is satisfied when x is equal to class 10 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

An alternating current can be produced by A a transformer class 12 physics CBSE

What is the value of 01+23+45+67++1617+1819+20 class 11 maths CBSE

Give 10 examples for herbs , shrubs , climbers , creepers