Exams

The first person shakes hands with 22 different people, the second person also shakes hands with 22 different people, but one of those handshakes was counted in the 22 for the first person, so the second person actually shakes hands with 21 new people. The third person, 20 people, and so on...
So,
22 + 21 + 20 + 19 + 18 + 17 + 16 + 15 + 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1
= n(n+1)/2 = 22 x 23 /2 = 11 x 23 = 253.

If earlier he is getting Rs. 1  per hr and working for 1 hr, income = Rs. 1
Now he is getting Rs 1.3333 per hr and working for 0.66667 hrs

Then income for 0.66667 hrs = Rs. 0.8889.

If payment per hr is increased by 33.33 %  and working hours dereased by 33.33%, then 11.11 % decrease in income.

1/K + 1/L + 1/M = 1/8 (Given)
Also given that K = 2L and L = 2M
=> 1/2L + 1/L + 2/L = 1/8
=> (1 + 2 + 4)/2L = 1/8
=> 2L/7 = 8
=> L = 28 hours.

The partition of the Indian subcontinent into India and Pakistan after World War-II along the ''Radcliffe line'' following the Indian Independence Act of 1947 was based on religion conflicts.

Pakistan was a Muslim-majority country, while India's population consisted mostly of Hindus. Originally, Pakistan was divided into two regions, East Pakistan and West Pakistan. However, East Pakistan won its independence in 1971, and is now called Bangladesh.

Let age of retirement = S
so according to the given condition 25000(x-20)
=10000 x 3 + 12000 + 14000 + 16000 + 18000 + 20000 + 22000 + 24000 + 26000 + 28000 + 30000 + 30000(S-33)
= 30000 + 210000 + 30000S-990000
= 30000S - 750000
or 25000S - 500000 = 30000x - 750000
or 5000x = 250000
or S = 50 yrs.

In the given series, 

 2nd term = 1st term + 12= 4 +1 = 5  

3rd term = 2nd term + 22 =5+4= 9  

4th term = 3rd term + 32 =9+9=18  

5th term = 4th term + 42 = 18+16=34 

Therefore, odd term is 32

In common we all call the systematic name of NH4ClO3 as Ammonium Chlorate. But originally the systematic name is azanium trioxidochlorate.