Two vessels contain a mixture of water and lime. In the first vessel the volume of lime juice is 2/3 rd that of water. In the second vessel the volume of water is thrice that the lime juice. These two are mixed in a third vessel of 14 litres capacity, so that the volume of water is twice that of lime juice. What is the ratio of the mixture taken from the two vessels?
Answer: A In the first vessel, let the volume of water be 3k Litres, Lime juice is 2x Litres. In the second vessel, If p litres of lime juice is there, then water is 3p Litres. From alligation rule, the ratio of two mixture is 3/5....................3/4(Quantity mixed) ..........2/3............ (Average) 1/12..................1/15(ratio's) Thus = 5:4.
Q. No. 2:
Sumit works as a state contractor for PWD and supplies bitumen mix for road construction. He hastwo varieties of bituman, one at Rs. 42 per kg and the other at Rs. 25 per kg. How many kg of firstvariety must Sumit mix with 25 kg of second variety,. So that he may, on selling the mixture at 40kg, gain 25% on the outlay?
Answer: D The problem statement misses the word “per”. The last sentence should have had“....mixture at Rs. 40 per kg …” Cost price of mixture = 40/1.25 = Rs 32/kg. Let the required ratio be x : y Average cost 42.......................25 Resultant cost...............32.............. Ratio x.........................y (42-32)/(32-25) = y/x x/y = 7/10 = x/25 => x = 250/7
Q. No. 3:
Ashok a master adulterator cum grosser sells haldi powder (turmeric powder), which contains fivepercent saw dust. What quantity of pure haldi should be added to two kilos of haldi (containing fivepercent saw dust) so that the proportion of saw dust becomes four percent?
Answer: C Pure haldi has 0% saw dust and the adulterated sample has 5% saw dust in it. By adding appropriate amount of pure haldi, the concentration of saw dust, in the 5% sample, can be reduced to 4 %. Applying allegation: 5%..............................0%(Pure haldi) .................4......................(Resultant) 4..................................1 (Ratio) => 4/1 = 2kg(of 5% sample) /Pure haldi => Pure haldi = 0.5 kg.
Q. No. 4:
In a mixture of 35 litre, the ratio of petrol to alcohol is 4:1. If 7L alcohol is added to the mixture, the ratio of petrol to alcohol changes to a new ratio. If we want the ratio of petrol to alcohol to change back to the original value, how much petrol is to be added now?
Answer: B In order to keep the solution of the same ratio, we need to add petrol in the same ratio as already there in the solution i.e, we need to add = 4/1 * 7 = 28 L
Q. No. 5:
A girl has 1L of solution that contains orange juice and water in the ratio 3:1. She adds 250ml of 3:2 solution of orange juice and water to it and then use 250ml of the combined mixture to make complete juice. How much of pure juice is she left with?
Answer: D In a mixture 1000 ml, orange juice: water = 3:1 Hence, orange juice = 750 ml and water = 250 ml A 250 ml of 3:2 solution contains 150 ml of juice and 100 ml water. Total juice = 900 ml , total water = 350 ml After using 250 ml to make impure juice used = 250/1250 * 900 = 180 ml Pure juice left = 900 - 180 = 720 ml
Q. No. 6:
Several litres of Water were drawn from a 54 L vessel full of water and an equal amount of acid is added. Again the same volume of the mixture was drawn off and replaced by acid. As a result, the vessel contained 24L of pure water. How much water was drawn off initially?