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SAI International School
                                                      CLASS - VIII

               Mathematics
               CHAPTER-2: Linear Equation in one variableLesson Notes-4




               SUBTOPICS : SOME MORE APPLICATIONS




               General form a 2-digit number ‘ab’  is 10a + b
               If the digits of the number is reversed like ‘ba’ then it becomes 10b+a


               Example 1: The digits of a two-digit number differ by 3. If the digits are interchanged,
               and the resulting number is added to the original number, we get 143. What can be the
               original number?



               Solution: Take, a two-digit number, say, 56. It can be written as 56= (10×5) + 6.

               If the digits in 56 are interchanged, we get 65, which can be written as (10 × 6 ) + 5.

               Let us take the two digit number such that the digit in the units place is b.
               The digit in the tens place differs from b by 3. Let us take it as b + 3.

               So the two-digit number is 10 (b + 3) + b = 10b + 30 + b = 11b + 30.

               With interchange of digits, the resulting two-digit number will be 10b + (b + 3) = 11b +
               3.

               If we add these two two-digit numbers, their sum is

               (11b + 30) + (11b + 3) = 11b + 11b + 30 + 3 = 22b + 33
               It is given that the sum is 143.

               Therefore, 22b + 33 = 143

               or 22b = 143 – 33
               or 22b = 110

               or b = 110÷22

                                or  b = 5

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