Question

The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?

Answer 1

let x be the larger number and y be the smallest one. it says, x-y=1365---------(1) and also says x/y=6 leaving remainder 15.
x / y= 6  =>x= 6 * y--------(2)    
substitute equation 2 in equation 1, it'll become 
[6*y] -y=1365  {cauz value of x=6*y}   now, 6y-y=5y right?? so we'll say 
5y=1365------(3)  => y=1365/5 which is 273  therefore y= 273. Now the rest is easy!
substitute y in equation 2, that is x=6*y => x=6*273 and that is x=1638
now to confirm, 1638-273=1365 and divide x/y, you will get 6!!! hurray u got the answer. y is the smaller number=273

Answer 2

Answer:

y-x=1365

x/y=quotient=6

remainder=15

qr/d=

6 15/x=

y=6x+15

6x+15-x=1365

6x-x+15=1365

5x=1365-15

5x=1350

x=270