Question

A number when divided by 3, 5, and 7 successively in order gives remainder 2, 3, and 4 respectively. If it is then divided by 105, the remainder will be-

Answer 1

Number = x

x ÷  3 = P as quaotient   (2reminder)    ...........(1)

P ÷ 5 = Q as quotient  (3reminder)   ............(2)

Q ÷ 7 =  R as quotient (4 as reminder) .......(3)

From (3)   Q = 7R + 4

From (2)    P = 5Q + 3   =  5(7R+4) +3 = 35R + 20 + 3 = 35R + 23

From (1)   x = 3P + 2   = 3(35R + 23) + 2 = 105R + 69 + 2 = 105R + 71

Now the number is 105R + 71

So   105R + 71    =

              105

when 105R/105 there will be no reminder because the number 105R will be the multiple of 105. So  reminder will come 71.