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

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.

Right Option : C
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Explanation
Question : 2

A two digit number is four times the sum of its digits and twice the product of the digits. Find the number.

Right Option : B
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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.

Right Option : A
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Explanation
 
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