Question:21.What least number be added to 3000 to obtain a number exactly divisible by 19?
On dividing 3000 by 19, we get 17 remainder. :. Number to be added =(19-17)=2.
Question:22.Find the number which is nearest to 3105 and exactly divisible by 21.
On dividing 3105 by 21,we get 18 as remainder. :. number to added to 3105 is (21-18)=3 :. 3108 the required number.
Question:A number when divided by 342 gives a remainder 47.when the same number is divided by 19,what would be the remainder ?
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.Question:24.(i) `? ÷ 147 = 29` (ii) `? xx 144 = 12528`
(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.
Question:How many numbers between `11` and `90` are divisible by `7`?
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`