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

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
View Explanation

Question : 2

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 : 3

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

Video Link - Have a look !!!

Language - English

Chapters

Polynomial I

Polynomials II

Pair of Linear Equations I

Pair of Linear Equations II

Real Numbers I

Real Numbers II

Coordinate Geometry I

Coordinate Geometry II

Quadratic Equations I

Quadratic Equations II

Introduction to Trigonometry I

Introduction to Trigonometry II

Arithmetic Progression I

Arithmetic Progression II

Introduction to Trigonometry

Some Applications of Trigonometry

Statistics I

Statistics II

Surface Area and Volume I

Surface Area and Volume II

Areas Related to Circles

Direct and Inverse Variation

Partnership and Mixture

Content / Category

IMO-Mathematics Olympiad

Central Government Service

ISO - Science Olympiads

State Government Services

Banking And Insurance

Railways & Metro Services

MBA Entrance

Law Entrance

English Proficiency

Reasoning Proficiency

Computer Proficiency

Navodaya Entrance 6th & 9th

Sainik School Entrance

Class / Course

Students / Parents Reviews [20]

Usually we see institutes offering objective based learning which usually causes a lag behind in subjective examinations which is the pattern followed by schools. I think it is really a work of planning to make us students grab the advantages of modes of examination, Objective Subjective and Onli...

Anika Saxena

8th

Abhyas is an institute of high repute. Yogansh has taken admission last year. It creates abilities in child to prepare for competitive exams. Students are motivated by living prizes on basis of per...

Yogansh Nyasi

7th

It was good as the experience because as we had come here we had been improved in a such envirnment created here.Extra is taught which is beneficial for future.

Eshan Arora

8th

We started with lot of hope that Abhyas will help in better understnding of complex topics of highers classes. we are not disappointed with the progress our child has made after attending Abhyas. Though need to mention that we expected a lot more. On a scale of 1-10, we would give may be 7.

Manya

8th

Abhyas Methodology is very good. It is based on according to student and each child manages accordingly to its properly. Methodology has improved the abilities of students to shine them in future.

Manish Kumar

10th

It has a great methodology. Students here can get analysis to their test quickly.We can learn easily through PPTs and the testing methods are good. We know that where we have to practice

Barkha Arora

10th

My experience with Abhyas academy is very nice or it can be said wonderful. I have been studying here from seven class. I have been completing my journey of three years. I am tinking that I should ...

Hridey Preet

9th

Third consective year,my ward is in Abhyas with nice experience of admin and transport support.Educational standard of the institute recumbent at satisfactory level. One thing would live to bring in notice that last year study books was distributed after half of the session was over,though study ...

Ayan Ghosh

8th

My experience was very good with Abhyas academy. I am studying here from 6th class and I am satisfied by its results in my life. I improved a lot here ahead of school syllabus.

Ayan Ghosh

8th

It was a good experience with Abhyas Academy. I even faced problems in starting but slowly and steadily overcomed. Especially reasoning classes helped me a lot.

Cheshta

10th

My experience with Abhyas academy is very good. I did not think that my every subject coming here will be so strong. The main thing is that the online tests had made me learn here more things.

Hiya Gupta

8th

The experience was nice. I studied here for three years and saw a tremendous change in myself. I started liking subjects like English and SST which earlier I ran from. Extra knowledge gave me confi...

Aman Kumar Shrivastava

10th

In terms of methodology I want to say that institute provides expert guidence and results oriented monitering supplements by requsite study material along with regular tests which help the students to improve their education skills.The techniques of providing education helps the students to asses...

Aman Kumar Shrivastava

10th

Abhyas institute is one of the best coaching institute in the vicinity of Ambala cantt.The institute provides good and quality education to the students.The teachers are well experienced and are v...

Abhyas institute is one of the best coaching institute in the vicinity of Ambala cantt.The institute provides good and quality education to the students.The teachers are well experienced and are very helpful in solving the problems. The major advantages of the institute is extra classes for weak...

Shreya Shrivastava

8th

Abhyas is good institution and a innovative institute also. It is a good platform of beginners.Due to Abhyas,he has got knoweledge about reasoning and confidence.My son has improved his vocabulary ...