Question
Download Solution PDFFind 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.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The number between 550 and 700 such that when they are divided by 12, 16, and 24, leave the remainder 5 in each case
Concept Used:
LCM is the method to find the Least Common Multiples
Calculations:
⇒ 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.
Shortcut Trick Option elimination method: Subtract the remainder of 5 in every no means in the option 15 we have to subtract because the sum of the three numbers is given.
In this case only 3, no is a possible case
So we have to subtract 15 and then check the divisibility of 16 and 3.
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