SOLVED EXAMPLES FOR 16 TO 20

Ex.16 what lest number must be subtracted from 1672 to obtain a number which is completely divisible by 17?

Sol. 17) 1672 (98

 153

  142

   136

     6                 NUMBER TO BE SUBTYRACTEDF =6.

Ex. 17. What least number must be added tp 2010 to obtain a number which is completely divisible by 19?

Sol. 19) 2010 (105

19

  110

     95

      15        number to be added = (19 - 15) = 4

Ex. 18. On dividing 12401 by a certain number, we get 76 as quotient and 13 as remainder what is the divisor?

Sol. [(divisor)x (quotient)] + remainder = dividend

Divisor = (dividend) – (remainder)

                            Quotient

                                        3097 =163

= (12401 – 13) = 12388                                     =163

         76                    76   19  = 1

A = 163

Ex. 19 on dividing a certain number by 342, we get 47 as remainder. If the same number is divide by 18, what will be the remainder?

Sol. Suppose that the on dividing the given number by 342, we get quotient = k and remainder = 47. Then,

Number = 342 k + 47

= (18 + 19k ) + (18 x 2 ) + 11

=18 + (19k + 2 ) + 11.

So, the number when divided by 18 gives remainder = 11.

Ex. 20. Simplify:

 789 x 789 x 789 x 211 x 211        =?     

789 x 789 - 789 + 211 x 211

Sol. Given ex. P.  = (789)ᶟ + (211)ᶟ

                                    (789)² - (789 – 789 x 211 x 211)²

                               = (a² + b²)                                    

                                  (a² - ab + b²) ‘                  where a = 789 and b = 211

                       

                        (a + b) = (789 + 211 ) = 1000.