Solution :

Let the weight of full bottle be 6kg.

Therefore, weight of empty bottle is 1kg and that of water is 5kg.

If x% of water is removed, the weight of the bottle becomes 2kg.

Therefore, the amount of water removed is 4kg.

% of water removed = 4/5 *100 = 80%

Solution:

If the selling price of mixture is Rs.30/kg and the merchant makes a profit of 20%, then the cost price of the mixture = 30/1.2 = Rs.25/kg. 

We need to find out the ratio in which the three varieties are mixed to obtain a mixture costing Rs.25 /kg. 

Let variety A cost Rs.20/kg, variety B cost Rs.24 / kg and variety C cost Rs.30/kg. The mean desired price falls between B and C.

Step 1: 

Find out the ratio Qa:Qc using alligation rule. Qa/Qc=(30−25)/(25−20)=1/1

Step 2:

 Find out the ratio Qb:Qc using alligation rule.   Qb/Qc=(30−25/25−24)=5/1

Step 3: 

Qc is found by adding the value of Qc in step 1 and step 2 = 1 + 1 = 2

Therefore, the required ratio = 1 : 5 : 2

If there are 2 kgs of the third variety in the mixture, then there will be 5 kgs of the second variety in the mixture.

Note: When appearing in actual exam problems of this kind are to be skipped, at least in the first go. If you were able to solve decent number of other problems, then you should look at this problem.

Solution:

Assume there are 360 units of work (LCM of 40,60 and 12). 

Hence, A,B and C can do 4,9 and 30 units per day or together 43 units every 3 days.

So In 24 days, 43×8=344 units of work is completed. In the next 2 days, 13 units are completed and on 27th day, C takes (1/10)th of a day to finish the rest.

So, A and B worked for 9 days each and have hence put in 36 and 81 units respectively, and the rest of the 243 units is put in by C.

The wages shall also be distributed in the same ratio as:

Rs 36, Rs 81 and Rs 243