# The digits of a two-digit number differ by 3 .If the digits are interchanged and the resulting number is added to the original number we get 143 .What can be the original number?

Last updated date: 23rd Mar 2023

•

Total views: 309.3k

•

Views today: 6.86k

Answer

Verified

309.3k+ views

Hint: - If there is a two digit number it means there are two places, ones and tens. For solving questions let assume the digit at any place be x and then apply the condition of the question to solve further.

Here in the given question there is a two digit number it means it has two places once place and tens place.

Now, let the digit at tens place be x.

Then the digit at once place be (x+3) as in the question it is given that the other digit is differ by 3.

Tens place=x

Once place= (3+x)

Therefore the two digit number forms by these two digits is

Number= 10x+1(x+3) as we know that for forming a two digit number we multiply the digit at tens place by 10 and then add it with the digit at once place by multiplying 1 at once place.

Therefore the required number is 11x+3

Now according to question we interchange the numbers,

i.e. tense place become= (3+x) and once place became=x

The new number formed is, Number= 10(x+3) +x

Therefore new number=11x+30

Now in the question it said if we add old number and new numbers it become 143

i.e. 11x+3+11x+30=143

$

\Rightarrow 22x + 33 = 143 \\

\Rightarrow 22x = 110 \\

\Rightarrow x = \frac{{110}}{{22}} \\

\therefore x = 5 \\

$

Now put the value of x in the required number,

$\therefore $Required number is $11x + 3 = 11 \times 5 + 3 = 58$

Note: - Whenever we face such a type of question the key concept for solving the question is first assume the digits at any place and then form the numbers by these digits according to the question. And then apply the statement of question to proceed a d then we will find the value of that digit. Now put the value of that digit to get the number.

Here in the given question there is a two digit number it means it has two places once place and tens place.

Now, let the digit at tens place be x.

Then the digit at once place be (x+3) as in the question it is given that the other digit is differ by 3.

Tens place=x

Once place= (3+x)

Therefore the two digit number forms by these two digits is

Number= 10x+1(x+3) as we know that for forming a two digit number we multiply the digit at tens place by 10 and then add it with the digit at once place by multiplying 1 at once place.

Therefore the required number is 11x+3

Now according to question we interchange the numbers,

i.e. tense place become= (3+x) and once place became=x

The new number formed is, Number= 10(x+3) +x

Therefore new number=11x+30

Now in the question it said if we add old number and new numbers it become 143

i.e. 11x+3+11x+30=143

$

\Rightarrow 22x + 33 = 143 \\

\Rightarrow 22x = 110 \\

\Rightarrow x = \frac{{110}}{{22}} \\

\therefore x = 5 \\

$

Now put the value of x in the required number,

$\therefore $Required number is $11x + 3 = 11 \times 5 + 3 = 58$

Note: - Whenever we face such a type of question the key concept for solving the question is first assume the digits at any place and then form the numbers by these digits according to the question. And then apply the statement of question to proceed a d then we will find the value of that digit. Now put the value of that digit to get the number.

Recently Updated Pages

If abc are pthqth and rth terms of a GP then left fraccb class 11 maths JEE_Main

If the pthqth and rth term of a GP are abc respectively class 11 maths JEE_Main

If abcdare any four consecutive coefficients of any class 11 maths JEE_Main

If A1A2 are the two AMs between two numbers a and b class 11 maths JEE_Main

If pthqthrth and sth terms of an AP be in GP then p class 11 maths JEE_Main

One root of the equation cos x x + frac12 0 lies in class 11 maths JEE_Main

Trending doubts

What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?