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
View Explanation

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
View Explanation

Question : 3

A two digit number such that the product of its digits is 21. When 36 is subtracted from the number the digits are interchanged. Find the digit at the tens place.
A. 7	B. 77	C. -7	D. NONE F THESE
Right Option : A
View Explanation

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Solving Statements For A Two Digit Number

Solving Statements For A Two Digit Number

Students / Parents Reviews [20]

Upmanyu Sharma

Manya

Aman Kumar Shrivastava

Anika Saxena

Cheshta

Barkha Arora

Aman Kumar Shrivastava

Manish Kumar

Ayan Ghosh

Hridey Preet

Shivam Rana

Sharandeep Singh

Aman Kumar Shrivastava

Hiya Gupta

Barkha Arora

Yogansh Nyasi

Eshan Arora

Shreya Shrivastava

Prisha Gupta

Yatharthi Sharma