Question

A number when divided by m leaves the remainder of 9 and when divided by 3m leaves a remainder of 36.what is tge remainder left when twuce the nymber is divided by 3m ?

Answer 1

discount cousin in of shock sinc

Answer 2

Thee remainder left when twice the number is divided by 3m is 72

Solution:

Given, a number when divided by "m" leaves the remainder of 9  

And when divided by 3m leaves a remainder of 36.

We have to find what is the remainder left when twice the number is divided by 3m  

Let the number be “n”  

Given its divided by “m” and leaves remainder 9.  

Lets assume the quotient be x.  

So that n=mx+9 → (1)

Similarly n when divided by 3m leaved remainder 36.  

Lets assume the quotient be y.  

So that n=3my+36  

Equating the above 2, we get mx+9 = 3my+36  

mx-3my = 36 – 9  

m(x-3y) = 27

m(x-3y) = 9 x 3 or 27 x 1

By comparing m = 9 or 3 or 27 or 1 and x – 3y = 3 or 9  or 27 or 1.  

If we observe, m can’t be 9, 3, 1, as if it is 9 or 3 or 1, then remainder cannot be 9.

So, m = 27 and x - 3y = 1

let x = 4 and y = 1 to satisfy x – 3y = 3

Now, substitute m and x values in (1)

n = 27 x 4 + 9 = 117

Now, when twice the number (i.e. 2 x 117 = 234) is divided by 3m (i.e. 3 x 27 = 81) it leaves the remainder → 234 – 81 x 2 [81 is multiplied with 2 because, 81 x 3 would become more than 234.

Hence, the remainder is 72.