Question

Un te sales Rumber which when divided by 14, 28 and 56 leaves
(a) Find the smallest number that leaves 5 as remainder when divided by
(b) Find the smallest number which when reduced by 2 becomes divisib
What is the smallest number of chairs that can be arranged in
rows of 9 or 15?
5. Jack and Jill stand on the same tile of a tiled floor. Jack starts jumping
to every third tile in a row. And Jill starts jumping to every second
tile in that row. Which is the first tile on which both land?
6. The alarms on two mobile phones ring together once. If one
rings every 15 minutes and the other rings every 25 minutes,
after how many minutes will they ring together again?
51​

Answer 1

Answer:

Let the smallest number be X.

X=9 (mod 15)

X=9 (mod 20)

X=9 (mod 48)

LCM of {15,20,48}=240

Since the REMAINDER is same (9) , so the above congruences are consistent if the modulo is the LCM of all the moduli.

X=9 (mod 240)

Expressing the above congruence in Parametric Form, we get

X= 9 + 240 t where t is any integer.

Take t =0

X=9 : 9 is the 1st lowest +ve Number.(Part Ans.)

Take t= - 1

X= -231 : (-)231 is the highest -ve number.

Please note that we can take t equal to any -ve integer (upto Infinitum ) to arrive at a -ve solution. So the Answer is INFINITY ,if -ve number is permitted . □ANSWER.