8: find the greatest number if 5 digit which when divided by 25,30and 40 leaves a remainder of 20, 25 and 35 respectively.

Let us find the LCM of the given numbers 25,30 ,40

Lcm= 600

The difference in numbers from the remainder are

25-20=5

30-25=5

40-35=5

The remainder in each case is 5 less than the divisor

The greatest 5 digit number divisible by 5 is 99995

Dividing this by LCM 600

=167(rounded)

Let n+5 leaves remainder 5 when divided by 25,30,40

n+5=167 times 600

n+5=99600

n=99595

The 5 digit greatest number divided by 25,30and 40 leaving a remainder of 20, 25 and 35 respectively is 99595.

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,