Find tge greatest number of 5 digits which on being divided by 9,12,24 and 45 leaves 3,6,18 and 39 as remainders respectively.
Answers
The difference between the divisor and the remainder is same in all the cases which is 6
STEP 1:
LCM OF DIVISORS
LCM OF( 9,12,24,45) IS 360
STEP 2:
We know the largest five digit number is 99999
Now to find the largest five digit number which satisfy the given conditons then do the following
A) 360*N-6
N, is the quotient of 99999/360
U will get the answer as 360*277–6= 97214
B) Divide 99999/360
U will get remainder as 279
SUBTRACT 279 FROM 99999 WHICH IS 99720
Now 99720–6= 97214 which will be ur answer
OR
3=x mod 9
6=x mod 12
18=x mod 24
39=x mod 45
Modulo values in each case is number-6.
Number is LCM-6
=9*4*2*5–6
=360–6
=354
To find largest five digit number, 360x-6 where x is integer.
100000/360= 10000/36=277
Largets 5 digit number =360*277–6
=99720–6
=99714
This one was a bit tricky though.
Hope it was simple illustration.
Good luck and don't forget to upvote if you liked how it was solved.
Answer:
The difference between the divisor and the remainder is same in all the cases which is 6
STEP 1:
LCM OF DIVISORS
LCM OF( 9,12,24,45) IS 360
STEP 2:
We know the largest five digit number is 99999
Now to find the largest five digit number which satisfy the given conditons then do the following
A) 360*N-6
N, is the quotient of 99999/360
U will get the answer as 360*277–6= 97214
B) Divide 99999/360
U will get remainder as 279
SUBTRACT 279 FROM 99999 WHICH IS 99720
Now 99720–6= 97214 which will be ur answer
OR
3=x mod 9
6=x mod 12
18=x mod 24
39=x mod 45
Modulo values in each case is number-6.
Number is LCM-6
=9*4*2*5–6
=360–6
=354
To find largest five digit number, 360x-6 where x is integer.
100000/360= 10000/36=277
Largets 5 digit number =360*277–6
=99720–6
=99714
This one was a bit tricky though.
Hope it was simple illustration.
Good luck and don't forget to upvote if you liked how it was solved.
Step-by-step explanation: