Find the sum of the numbers between 550 and 700 such that when they are divided by 12, 16 and 24, leave remainder 5 in each case.

Find the sum of the numbers between 550 and 700 such that when they are divided by 12, 16 and 24, leave remainder 5 in each case.

a) 1998

b) 1887

c) 1788

d) 1884

Sol:

⇒ LCM of 12, 16, and 24 = 48 

Multiple of 48 bigger than 550 which leaves remainder 5 are 

⇒ 1st Number = 48 x 12 + 5 = 581 

⇒ 2nd Number = 48 x 13 + 5 = 629 

⇒ 3rd Number = 48 x 14 + 5 = 677 

⇒ Sum of these numbers are = 581 + 629 + 677 = 1887 

⇒ Hence, The sum of the numbers are 1887.