Question

professor absentminded has a very peculiar problem that he cannot remember number larger than 15. however he tells his wife, i can remember any number up to 100 by remembering the three numbers obtained as remainder when the numbers is divided by 3,7 and 11 respectively. for example (2,3,6)is 17. professor remembers that he had(2,4,8)rupees in the purse, and he paid(2,5,4) rupees to the servant. how much money is left in the purse?; professor absentminded has a very peculiar problem that he cannot remember number larger than 15. however he tells his wife, i can remember any number up to 100 by remembering the three numbers obtained as remainder when the numbers is divided by 3,7 and 11 respectively. for example (2,3,6)is 17. professor remembers that he had(2,4,8)rupees in the purse, and he paid(2,5,4) rupees to the servant. how much money is left in the purse?

Answer 1

Answer:

Step-by-step explanation:

Wtf

LET THE AMOUNT HE HAD BE X

IN THE QUESTION IT IS GIVEN THAT WHEN X IS DIVIDED BY 3,5,7 LEAVES REMAINDERS 1,1,6

LETS TAKE THE LAST NUMBER I.E 7

X%7=6...I.E THE NUM IS 7Y+6

POSSIBLE VALUES OF Y ARE FROM 1 TO 13

THEN X MAY BE FROM 13,20,27,....76,83,90,97

THEN DIVIDE THE ABOVE NUMS BY 3 AND 5 THE NUM WHICH LEAVES REMAINDERS 1,1 IS THE REQUIRED NUM

this might look like a big process but you can calculate the num in your mind.

HOPE THIS IS HELPFUL

THANK U

Answer 2

Answer:  56

Step-by-step explanation:

Let the money with the professor = N

Then N = 3a +1 = 5b + 1 = 7c + 6.

Solving the above we get N = 181

(Explanation: See LCM formula 1 and 2: Click here)

When a number is divided by several numbers and we got same remainder in each case, then the general format of the number is LCM (divisors).x + remainder.

In this case 3, 5 are divisors. So N = 15x + 1. Now we will find the number which satisfies 15x + 1 and 7c + 6.

⇒ 15x + 1 = 7c + 6  ⇒ c = $\dfrac{{15x - 5}}{7}$ ⇒ c = $2x + \dfrac{{x - 5}}{7}$

Here x = 5 satisfies. So least number satisfies the condition is 5(15)+1 = 76.

(x = 12 also satisfies condition. So substituting in 15x + 1 we get, 181 which satisfies all the three equations but this is greater than 100)

Similarly Money given to servant = M = 3x + 2 = 5y = 7z + 6

Solving we get M = 25.

(125 also satisfies but this is next number)

Now N - M = 56