what will be the highest three digit number which when divided by 3,7 and 27 leves remainder 2 ?
Answers
Answer:
what will be the highest three digit number which when divided by 3,7 and 27 leves remainder 2 ?
Step-by-step explanation:
The answer is 983.
The number when divided by 6 should give a remainder as 5. I can therefore write the number as 6x + 5 where x is the quotient when the number is divided by 6 and 5 is the remainder. Similarly when divided by 5 should give a remainder as 3. the same number can also be written as 5y + 3 where y is the quotient when the number is divided by 5 and the remainder is 3.
Since the number is same we can equate it as 6x+ 5 = 5y +3 or 6x = 5y-2 since x and y are quotients it cant be in fractions the smallest value of y that can satisfy the equation is 4 and y will be 3
When we sustitute 3 and 4 for x and y respetively in the term 6x+ 5 or 5y+ 3 you will get the term as 23. the least value satisfying the question is 23 but the question mentions about largest three digit number.
In the equation 6x + 5 = 5y + 3 the quotients x and y are geting multiplied 6 and 5 respectively. So find out the LCM of 6 and 5 which is 30. Every number that is added to 23 in multiples of 30 (LCM of 6 and 5)will satisfy the condition like 23, 53, 83 113, etc.
Since we want the largest 3 digit number find out largest three digit number that is multiple of 30 and add 23 to it. The largest 3 digit number multiple of 30 is 990 but when you add 23 it becomes 1013 which is a 4 digit number and does not satisy the requirement of the question.
The number earlier to 990 which is mutiple of 30 is 960. Adding 23 to it the number will become 983. the answer is 983
HOPE THIS HELPS U
HAPPY NEW YEAR☺