# A two digit number is such that the product of its digits is 18. When 63 is subtracted from the number. the digits interchange their places. Find the number.

Last updated date: 20th Mar 2023

•

Total views: 213.7k

•

Views today: 3.92k

Answer

Verified

213.7k+ views

Hint: To convert the digits to numbers, we need to multiply with the digit with the place value of the digit. For example, the value of the number formed by the digit 4 in the ten’s place and the digit 3 in the one’s place is $4 \times 10 + 3 \times 1 = 43$.

Complete step-by-step answer:

Let the digit at unit’s place be x

Let the digit at ten’s place be y

Given, the product of digits of a number is 18.

$

x \times y = 18 \\

\Rightarrow y = \dfrac{{18}}{x} \\

$

So, the digit at ten’s place is $\dfrac{{18}}{x}$ .

Required number $ = \dfrac{{18}}{x} \times 10 + x \times 1$

If digits interchange their places. So, the digit at the unit's place is $\dfrac{{18}}{x}$ and the digit at the ten's place is x.

Number formed by interchanging the digits $ = x \times 10 + \dfrac{{18}}{x} \times 1$

Now according to question,

$

\dfrac{{180}}{x} + x - 63 = 10x + \dfrac{{18}}{x} \\

\Rightarrow 180 + {x^2} - 63x = 10{x^2} + 18 \\

\Rightarrow 9{x^2} + 63x - 162 = 0 \\

\Rightarrow {x^2} + 7x - 18 = 0 \\

$

Now, factorize

$

\Rightarrow {x^2} + 9x - 2x - 18 = 0 \\

\Rightarrow x\left( {x + 9} \right) - 2\left( {x + 9} \right) = 0 \\

\Rightarrow \left( {x - 2} \right)\left( {x + 9} \right) = 0 \\

\Rightarrow x = 2, - 9 \\

$

Digit can’t be negative So, we eliminate x=-9

Now, we get x=2

Required number $ = \dfrac{{180}}{2} + 2 = 90 + 2 = 92$ .

Note: Whenever we face such types of problems we use some important points. First we assume the digit at units and tens place and convert the digits into numbers by the method used above, then after solving the equation we can get the required answer.

Complete step-by-step answer:

Let the digit at unit’s place be x

Let the digit at ten’s place be y

Given, the product of digits of a number is 18.

$

x \times y = 18 \\

\Rightarrow y = \dfrac{{18}}{x} \\

$

So, the digit at ten’s place is $\dfrac{{18}}{x}$ .

Required number $ = \dfrac{{18}}{x} \times 10 + x \times 1$

If digits interchange their places. So, the digit at the unit's place is $\dfrac{{18}}{x}$ and the digit at the ten's place is x.

Number formed by interchanging the digits $ = x \times 10 + \dfrac{{18}}{x} \times 1$

Now according to question,

$

\dfrac{{180}}{x} + x - 63 = 10x + \dfrac{{18}}{x} \\

\Rightarrow 180 + {x^2} - 63x = 10{x^2} + 18 \\

\Rightarrow 9{x^2} + 63x - 162 = 0 \\

\Rightarrow {x^2} + 7x - 18 = 0 \\

$

Now, factorize

$

\Rightarrow {x^2} + 9x - 2x - 18 = 0 \\

\Rightarrow x\left( {x + 9} \right) - 2\left( {x + 9} \right) = 0 \\

\Rightarrow \left( {x - 2} \right)\left( {x + 9} \right) = 0 \\

\Rightarrow x = 2, - 9 \\

$

Digit can’t be negative So, we eliminate x=-9

Now, we get x=2

Required number $ = \dfrac{{180}}{2} + 2 = 90 + 2 = 92$ .

Note: Whenever we face such types of problems we use some important points. First we assume the digit at units and tens place and convert the digits into numbers by the method used above, then after solving the equation we can get the required answer.

Recently Updated Pages

If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts

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

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

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE