# Set Theory, Calendars, Clocks and Binomial Theorem

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## Sets and Unions

Sonu started a new business with accounts in two different banks (i.e. Axis and SBI).He deposited the earnings of each day in either of the two banks. However he does not deposit his earnings in both the banks simultaneously on any given day. However somehow he could not carry the business for long and had to shut it down. Find the total no of days Sonu carried on the business if… 1) He did not deposited in axis bank on 20 days and in SBI on 24 days.
2) He deposited on either axis bank or SBI on 28 days.
1. 36
2. 18
3. 13
4. 24

Choice A. 36

## Detailed Solution

Let the total No. of days Sonu deposited the earnings in Axis bank be ‘n(a)’ and that in SBI be ‘n(b)’
Now,
Total no of days he carried on the business = n(a) + n(b) – n(a∩b) + Neither (Days he didn’t earned)
Since on any given day he does not deposit in both the bank accounts
n(a∩b) = 0
Hence,
Total no of days he carried on the business = n(a) + n(b) + Neither (Days he didn’t earned)
Now
A/Q
Total – n(a) = 20……………………………(1)
Total – n(b) = 24……………………………(2)
n(a) + n(b) = 28………………………………(3)
Solving the 3 equations we get,
n(a) = 16
n(b) = 12
Total = 36
Hence the total number of days he carried on the business = 36 = (a) Ans.

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