Question

Find the greatest numbers of 5 digits which when divided
by 25, 30 and 40 leaves the reminder of 20, 25 , 35

Answer 1

Let the no. be x

1.We know that x=25a+20;where “a” is an integer ((when divided by 25 leaves remainder of 20))

2. x=30b+25;where “b” is an integer

3. x=40c+35;where “c” is an integer

Since x>/=10000 and “a” is integer,

By substituting x in “1”, a>/=400

From “1” and “2” AND “1” and “3”:

b=(25a−5)/30

c=(25a−15)/40

Substitute with values of a starting by 400 and adding 1 each time ((“a” is an integer)) until you have both “b” and “c” as integers.

a=407 will do it.

By substituting “a” in “1” , x=10195

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