Question

Find the smallest number when divided by 7,8 and 9 leaves a remainder 10, and is exactly divided by 11

Answer 1

Answer:

Step-by-step explanation:

sol: the no should be in a format  

7x+2 = 8y+4 = 9z+6

7x+2= 4(4y+1)=3(3z+2)

So the  no is multiple of 12  

let 12p  

12p = 8y+4  

so it is possible if p = 1,3,5, ....  2n -1 --------(i)

12p = 9z +6  

 

so it is possible if p = 2,5,8,... 3n-1 ------ (ii)

for above (i) and (ii)  equation  p = 6n-1 ------(iii)

12p = 7x+2  

so it is possible if p = 6,13,20,... 7n -1 ------ (iv)

from (iii) or (iv)  

p = 42(n-1)

so 12*(42*(n-1))

putting n =1  

12*41= 492  

Ans is 492  

492= 7*70+2

492= 8*61+4

492= 9*54+6