Question

a no . when divided by divisor leaves remainder 27 twice the no. divided by same divisor leaves remainder 3 . find the divisor

Answer 1

Answer :

Let dividend = a
And
Divisor = d

Given : when divided by divisor leaves remainder 27 , So we get

a = dx + 27 ----- ( 1 ) ( Here x is our quotient )

And

Twice the number divided by same divisor leaves remainder 3 , So we get

2a = dy + 3 -------- ( 2 ) ( Here x is our quotient )

Subtract equation 1 from equation 2 , we get

a = d ( y - x ) - 24

a + 24 =d ( y - x ) , Substitute value from equation 1 , we get

dx + 27 + 24 = d ( y - x )

dx +51 = d ( y - x )

dx +51 = d z , Here z = y - x , this is also an integer

z = x + $\frac{51}{d}$
So,
$\frac{51}{d}$ , Should be integer , So that is possible when d = 1 , 3 , 17 , 51

But divisor 1 , 3 and 17 can't give 27 as remainder , So

Our divisor = 51 ( Ans )