[24] If 9th of the month falls on the day preceding Sunday, then on what day will 1st of the month fall?

If 9th of the month falls on the day preceding Sunday, then on what day will 1st of the month fall?

Explanation:

Given N = 10p78pq is exactly divisible by 120.
Since the last digit of the dividend is 0, the last digit of N also should be 0.
Then obviously, q = 0.
i.e., N = 10p78p0
Now we have to find p.
We know 120 = 3 x 5 x 8 and 3, 5 and 8 are co-primes.
If N is divisible by 120 then it is divisible by 3, 5 and 8.
We know that, "If a number is divisible by 3 then the sum of its digits also divisible by 3"
Then, 1+ 0 + p + 7 + 8 + p + 0 = 16 + 2p
i.e., 16 + 2p must be divisible by 3
Then the possible values of p are 1,4,7,10,13 and so on
Since p is a digit, the possible values are 1, 4, 7
Now, N must be divisible by 8 also.
We know that, "If a number is divisible by 8 then its last 3 digits also divisible by 8"
Here 8p0 is a multiple of 8.
Now put all the above possible values of p then we have 8p0 = 810 or 840 or 870
From these, 840 is a multiple of 8.
Then the value of p = 4 and N = 1047840
Hence, the required sum = 1 + 0 + 4 + 7 + 8 + 4 + 0 = 24.

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