Several litres of acid were drawn off a 54L vessel full of acid and an equal amount of water added. Again the same volume of the mixture was drawn off and replaced by water. As a result the vessel contained 24 L of pure acid. How much of the acid was drawn off initially?

Answer: C If the container contains x units of liquid and y units o liquid is taken out. If this operation is repeated n times. the final quantity of the liquid in the container is x(1- y/x)^{n} Hence in this equation 24= 54(1- x/54)^{2} where x= amount of acid initially drawn off (1- x/54)^{2} = 24/54 = 4/9 (1- x/54) = 2/3 On solving, we get x=18.

Q. No. 2:

Rs 6500 were divided equally among a certain number of persons. Had there been 15 more persons each would have got Rs 30 less. Find the original number of persons

Answer: A Let there be originally x persons. Then share of each persons = Rs 6500/x Given, 6500/(x+15) = 6500/x - 30 6500/x - 6500/(x+15) =30 On solving we get x= 50.

Q. No. 3:

Rs 770 has been divided among A,B and C such that A receives 2/9th of what B and C together receives. Then A's share is

Answer: C Let the number of boys be x and number of girls be y. Then , x/y =B and y/x =G 3(B+G) = 3(x/y + y/x) As we know that p+1/p always greater than or equal to 2. Thus 3(B+G)>= 6.

Q. No. 5:

In a mixture of 45L the ratio of milk and water is 3:2. How much water must be added to make the ratio 9:1?

Answer: B Quantity of milk = 3/5 * 45 = 27 L Quantity of water = 2/5 * 45 = 18L Let x litre of water be added to get the ratio 9:11 Then, (18+x)/27 = 11/9 On solving it we get , x= 15

Q. No. 6:

The monthly income of two persons are in the ratio of 4:5 and their monthly expenditure are in the ratio of 7:9. If each saves Rs 50 a month, then what are their monthly incomes?

Answer: D Let the income of two persons be 4x and 5x and their expenses be 7y and 9y. Then, 4x-7y= 50 and , 5x-9y=50 On solving these two equations we get x=100 and y=50 The income of persons are Rs 400 and Rs 500