Solving Statements For A Two Digit Number

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

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
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Question : 2

Two numbers are in the ratio 5 : 3. If they differ by 18, then. The numbers are ________________
A. 45, 27	B. 25, 15	C. 35, 21	D. 65, 39
Right Option : A
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Question : 3

The 2 digit number which becomes (5/6) of itself when its digits are reversed. The difference in the digits of the number being 1, when the two digits number is
A. 45	B. 54	C. 36	D. None of these
Right Option : B
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