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Solving Statements For A Two Digit Number

Quadratic Equations - Concepts

Identifying Quadratic Equations

Factors of Quadratic Equation

Factorization by Middle Term Splitting

Factorization by Grouping of Terms

Factorization by Completing the Square

Quadratic Formula

Nature of Roots of Quadratic Polynomial

Equations Reducible to Quadratic Form

Statement sum Involing Quadratic Equations

Solving Statements Involving Age

Statement sums involving Coins

Solving Statements For A Two Digit Number

Class - Bank Clerical Prelims 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

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 : 2

Two numbers are such that the ratio between them is 3 : 5. If each is increased by 10, the ratio between the new numbers so formed is 5:7. Find the original numbers.
A. 12, 20	B. 20, 25	C. 25, 15	D. 15.12
Right Option : C
View Explanation

Question : 3

If the three numbers are in the ratio 2:3:5, so that the sum of their squares is 608. Find the numbers respectively.
A. 8,12, 20	B. 12, 8, 20	C. 20, 8, 12	D. 20,12,8
Right Option : A
View Explanation