1. Question:A number when divided by 342 gives a remainder 47.when the same number is divided by 19,what would be the remainder ? 

    Answer
    On dividing the given number by 342,let k be the quotient and 47 as remainder.
    Then, number `=342k+47`
                         `=(19x18k+19x2+9)=19(18k+2)+9`
          `:.`The given number when divided by 19,gives (18k+2) as quotient and 9 as remainder.






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  2. Question:24.(i) `? ÷ 147 = 29` (ii) `? xx 144 = 12528` 

    Answer
    (i) Let`x/147`=29.Then,`x = (147 xx 29) = 4263.`
      
     :.Missing number is 4263.
    
     (ii) Let`xx 144 =12528.`Then,x=`12528/144`=87.






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  3. Question:How many numbers between `11` and `90` are divisible by `7`? 

    Answer
    The required numbers are `14,21,28,35....77,84.`
    This is an A.P. with `a=14` and `d=(21-14)=7`.
    Let it contain n terms.
    Then,`T~n=84`
    `⇒ a+(n-1)d=84`
    `⇒ 14+(n-1) xx 7`
    `=84 or n=11`
    `:.` Required number of terms `=11`






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  4. Question:26.Find the sum of all odd numbers upto 100. 

    Answer
    The given numbers are `1,3,5,7.....99,`
    This an A.P with a=1 and d =2.
    Let it contain n terms.Then,
    `1+(n-1) xx 2=99 or n=50.`
    `:.`Required sum =`n/2 ("first terms" + "last terms")`
                           =`50/2 xx (1+99)=2500`.






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  5. Question:Find the sum of all `2` digit numbers divisible by `3`. 

    Answer
    All 2 digit numbers divisible by `3` are :
    
     `12,15,18,21,......99`.
    
     This is an A.P. with `a =12` and `d=3`.
    
     Let it contain n terms.Then,
    
     `12+(n-1) xx 3=99` or `n=30`.
    
     Required sum =`30/2 xx (12+99) = 1665`.






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