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Solving Statements For A Two Digit Number

Quadratic Equations II - Concepts

Factors of Quadratic Equation

Factorization by Completing the Square

Statement sum Involing Quadratic Equations

Solving Statements Involving Age

Statement sums involving Coins

Solving Statements For A Two Digit Number

Equations Reducible to Quadratic Form

Class - 9th Aus Edu Subjects

Concept Explanation

Solving Statements For A Two Digit Number

Solving Statements For a Two Digit Number: A two digit number consists of two digits one at unit's place and the other at ten's place. Then two express the number we will use the expanded form for conversion.

Example: A number consists of two digit whose sum is 8. If 18 is added to the number its digits are reversed. Find the number.

Solution Let ones digit be x.

Since the sum of the digits is 8. Therefore, tens digit = 8- x.

$large therefore$ Number $large =10times (8-x)+x=80-10x+x=80-9x$ ....(i)

Now, Number obtained by reversing the digit

The digit at units place will be = 8-x.

The digit at ten's place will be = x.

$large The; reversed ;Number =10times (x)+ 8-x=10x+8-x=9x+8$

It is given that if 18 is added to the number its digits are reversed.

$large therefore$ Number + 18 = Reversed Number

$large Rightarrow ;;80-9x+18=9x+8$

$large Rightarrow ;;98-9x=9x+8$

$large Rightarrow ;;98-8=9x+9x$

$large Rightarrow ;;90-18x$

$large Rightarrow ;;frac{18x}{18}=frac{90}{18}$

$large Rightarrow ;;x=5$

Putting the value of x in (i), we get

Number $large =80-9times 5=80-45=35$

Example: A two digit number is such that product of two digits is 14. When 45 is added to the number, the digits are reversed. Find the number.

Solution: Let ones digit be x.

Since the product of the digits is 14.

$large Therefore,; tens; digit;=frac{14}{x}$

$large therefore$ Number $large =10times (frac{14}{x})+x=frac{140}{x}+x=frac{140+x^2}{x}$ ....(i)

Now, Number obtained by reversing the digit

$large The; digit; at ;units; place ;will; be = frac{14}{x}.$

The digit at ten's place will be = x.

$large The; reversed ;Number =10x+ frac{14}{x}=frac{10x^2+14}{x}$

It is given that if 45 is added to the number its digits are reversed.

$large therefore$ Number + 45 = Reversed Number

$large frac{140+x^2}{x} +45 = frac{10x^2+14}{x}$

$large frac{140+x^2+45x}{x} = frac{10x^2+14}{x}$

$large 140+x^2+45x = 10x^2+14$

$large 140+x^2+45x - 10x^2-14=0$

$large -9x^2+45x + 126=0$

$large -9(x^2-5x -14)=0$

$large x^2-5x -14=0$

$large x^2-7x+2x -14=0$

$large x(x-7)+2(x-7)=0$

$large (x-7)(x+2)=0$

Either x = 7 or x = -2

As a digit can not be negative, So the digit at units place is 7

So the digit at tens place = 14/7 = 2

Hence the number = 27

Sample Questions

(More Questions for each concept available in Login)

Question : 1

A nu7mber consists of two digits whose sum is 9. If 27 is subtracted from the original number. its digits are interchanged. Then the original number is___________________.
A. 53	B. 45	C. 92	D. 63
Right Option : D
View Explanation

Question : 2

Sum of the digits of a two digit number is 9. When we interchange the digits, it is found that the resulting two digit new number is greater than the original number by 27. Then the two digit number is
A. 63	B. 36	C. 45	D. 54
Right Option : B
View Explanation

Question : 3

The sum of two numbers is 2490. If 6.5% of one number is equal to 8.5% of the other, the numbers are ______________
A. 1311, 1411	B. 1411, 1079	C. 1089, 1311	D. 1079, 1089
Right Option : B
View Explanation

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Solving Statements For A Two Digit Number

Solving Statements For A Two Digit Number

Students / Parents Reviews [10]

Prisha Gupta

Manish Kumar

Eshan Arora

Archit Segal

Shreya Shrivastava

Shivam Rana

Ayan Ghosh

Hiya Gupta

Om Umang

Cheshta