Tricks With Digits
Tricks With Digits
Trick 1:
Adding the number and its reverse number.
Step 1: Choose a 2 digit number. Let us take 34
Step 2: Now reverse the digits. We get 43
Step 3: Add the two digits . we get 34 + 43 = 77
Step 4 : Divide the sum by 11. We get 77 11 = 7
Step 5 : The quotient will always be equal to the sum of digits that is 3 and 4 in this case
Justification:
Consider a two digit number having ones and tens digits as b and a respectively. On reversing the digits of this number , we obtain a two digit number
.
In expanded form, we have
and,
Adding (i) and (ii) , we get
Thus, is completely divisible by 11 and the quotient is a+b.
Also, it is divisible by a+b and in that case the quotient is 11.
In other words, the sum of any two digit number and the number
by reversing its digits is completely divisible by
(i) the sum a+b of its digits and the quotient is 11.
(ii) 11 and the quotient is a+b i.e., the sum of its digits.
Trick 2:
Subtracting the number and its reverse number.
Step 1: Choose a 2 digit number. Let us take 28
Step 2: Now reverse the digits. We get 82
Step 3: Subtract the smaller number from the bigger number . We get 82 - 28= 54
Step 4 : Divide the difference by 9. We get 54 9 = 6
Step 5 : The quotient will always be equal to the difference of the greater digit and the smaller digit that is 8 and 2 in this case. 8 -2 = 6
Justification:
Consider a two digit number having ones and tens digits as b and a respectively. On reversing the digits of this number , we obtain a two digit number
.
In expanded form, we have
and,
Subtracting (ii) from (i) , we get
Thus, is exactly divisible by 9 and the quotient is a- b i.e. the difference of the digits.
Also, is exactly divisible by a- b (difference of digits) and the quotient is 9.
Illustration 1: Without performing actual addition and division find the quotient when the sum of 79 and 97 is divided by (i) 16 (ii) 11.
Solution: The two numbers 79 and 97 are such that one can be obtained reversing the digits of the other.
Therefore, their sum when divided by the sum of the digits i.e. 7 + 9 = 16, we obtain 11 as the quotient .
If the sum of these two numbers is divided by 11, we get 7 + 9 ( sum of the digits) =16 as the quotient.
Illustration 2 : Without performing actual calculation find the quotient when the difference of 73 and 37 is divided by (i) 4 (ii) 9.
Solution: The two numbers 73 and 37 are such that one can be obtained reversing the digits of the other.
Therefore, their difference 73 - 37 = 36 when divided by the difference of the digits i.e. 7 - 3 = 4, we obtain 9 as the quotient .
If the difference 73 - 37 = 36 is divided by 9, we get 7 - 3 ( difference of the digits) = 4 as the quotient.
Find the product of the quotient when the sum of 53 and 35 is divided by 8 and the difference of 53 and 35 is divided by 9. | |||
| Right Option : B | |||
| View Explanation | |||
Without performing actual addition and division find the quotient when the sum of 95 and 59 is divided by 11 | |||
| Right Option : C | |||
| View Explanation | |||
Without performing actual addition and division find the quotient when the sum of 28 and 82 is divided by 10. | |||
| Right Option : A | |||
| View Explanation | |||
Students / Parents Reviews [20]
Abhyas is a complete education Institute. Here extreme care is taken by teacher with the help of regular exam. Extra classes also conducted by the institute, if the student is weak.
Om Umang
10thMy experience with Abhyas is very good. I have learnt many things here like vedic maths and reasoning also. Teachers here first take our doubts and then there are assignments to verify our weak points.
Shivam Rana
7thMy 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
8thMy 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 join Abhyas Academy in tenth class as I am seeing much improvement in Maths and English
Hridey Preet
9thThe 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 confidence to overcome competitive exams. One of the best institutes for secondary education.
Aman Kumar Shrivastava
10thIt 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
10thAbhyas 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 because of Abhyas.Teacher have very friendly atmosphere also.
Manish Kumar
10thAbhyas 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 performance in Abhyas exams. He is satisfied with institute.
Yogansh Nyasi
7thMy experience with Abhyas Academy has been very good. When I was not in Abhyas whenever teacher ask questions I could not speak it confidently but when I came in Abhyas, my speaking skills developed and now I am the first one to give the answer of teachers question.
Upmanyu Sharma
7thWhen I have not joined Abhyas Academy, my skills of solving maths problems were not clear. But, after joining it, my skills have been developed and my concepts of science and SST are very well. I also came to know about other subjects such as vedic maths and reasoning.
Sharandeep Singh
7thAbout Abhyas metholodology the teachers are very nice and hardworking toward students.The Centre Head Mrs Anu Sethi is also a brilliant teacher.Abhyas has taught me how to overcome problems and has always taken my doubts and suppoeted me.
Shreya Shrivastava
8thIt 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
8thIt 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
10thAbhyas academy is great place to learn. I have learnt a lot here they have finished my fear of not answering.It has created a habit of self studying in me.The teachers here are very supportive and helpful. Earlier my maths and science was good but now it has been much better than before.
Barkha Arora
10thUsually 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
8thAbhyas 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
8thBeing a parent, I saw my daughter improvement in her studies by seeing a good result in all day to day compititive exam TMO, NSO, IEO etc and as well as studies. I have got a fruitful result from my daughter.
Prisha Gupta
8thMy 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
8thAbhyas institute is one of the best coaching institute in the vicinity of Ambala Cantt area. The teachers of the institute are well experienced and very helpful in solving the problems of the students.The good thing of the institute is that it is providing extra classes for the students who are w...
Aman Kumar Shrivastava
10thThird 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 ...
