Question

Q19. A three-digit number was divided successively in order by 4, 5 and 6 leaving out the remainders. The remainders were respectively 2, 3 and 4. How many such three digit numbers are possible?

Answer 1

lcm = 60

three digit no = 60k + L

now divide byb 4,5,6 taking quotient as -1
as difference becomes 2 which is there 4-2 = 2, 5-3=2,6-4=2
take negative sign of l as quotient is taken as -1

so it will come negative

so three digit no= 6O k -2
take k= 2,3,4,5,6,7,8,9,10,---------15,16,

as 60×17 -2= 1018

so till 16 take

so no of 3 digit no= 15