Find the greatest number of 5 digits which when divided by 25, 30, and 40 leaves a remainder of 20, 25, and 35 respectively.​

Sure, here are the steps to find the greatest number of 5 digits which when divided by 25, 30, and 40 leaves a remainder of 20, 25, and 35 respectively:

Step 1: Find the least common multiple (LCM) of 25, 30, and 40. The LCM of these numbers is 600.

Step 2: The number we are looking for is of the form 600k + 20 (since the remainders when divided by 25, 30, and 40 are 20, 25, and 35 respectively, and 20 is the smallest among them).

Step 3: The greatest 5-digit number is 99999. So, we need to find the greatest number 'k' such that 600k + 20 <= 99999.

Step 4: Solving the inequality 600k + 20 <= 99999 gives k <= 166.63. Since 'k' has to be an integer, the greatest possible value for 'k' is 166.

Step 5: Substituting k = 166 in the equation 600k + 20 gives the number as 99620.

So, the greatest number of 5 digits which when divided by 25, 30, and 40 leaves a remainder of 20, 25, and 35 respectively is 99620.