Question for Practice Questions Level 2: Mixtures & Alligations - 1
Try yourself:Two liquids A and B are in the ratio 5 : 1 in container X and in the ratio 1 : 3 in container Y. In what ratio should the contents of the two containers be mixed so as to obtain a mixture of A and B in the ratio 1 : 1?
Explanation
Let X units of liquid be taken from container X.
So, liquid A taken = (5/6)X
Liquid B taken = (1/6)X
Let Y units of liquid be taken from container Y.
So, liquid A taken = (Y/4)
Liquid B taken = (3/4)Y
So, as the ratio is 1 : 1, we get
(5/6)X + (Y/4) = (X/6) + (3/4)Y
Or X/Y = 3/4
Hence, the required ratio is 3 : 4.
Thus, option d is correct.
Question for Practice Questions Level 2: Mixtures & Alligations - 1
Try yourself:A giant watermelon weighs 30 kg, of which 90% is water. After remaining in the sun for one hour, some of the water evaporates such that water makes up 80% of the weight. What is the weight of the watermelon now?
Explanation
Water portion of the watermelon weighs 90% of 30 = 27 kg.
Solid portion of the watermelon weighs 30 - 27 = 3 kg.
When water is 80%, solid portion = 20%
As 20% = 3 kg;
Total weight = 3 x 5 = 15 kg
Question for Practice Questions Level 2: Mixtures & Alligations - 1
Try yourself:In what ratio must water be mixed with milk to gain on selling the mixture at cost price? Explanation
Let the C.P. of 1 litre milk be Re. 1.
S.P. of 1 litre of mixture = Re. 1
Gain =
C.P. of 1 litre of mixture = (100 x 3/350 x 1) = Rs. 6/7
So, 6/7 litres of milk is present in 1 litre of mixture.
Hence, ratio of water to milk = 1/7 : 6/7 = 1 : 6
Alternate Solution:
To make a profit of 16.67% we need to add 16.67% water.
i.e. we need to add water in milk in the ratio 1 : 6.
Question for Practice Questions Level 2: Mixtures & Alligations - 1
Try yourself:In what proportion must wheat at Rs. 1.8 per kg be mixed with wheat at Rs. 2.5 per kg to get a mixture worth Rs. 2.0 per kg?
Explanation
Applying the rule of alligation:
⇒ Required ratio = 5 : 2
Question for Practice Questions Level 2: Mixtures & Alligations - 1
Try yourself:A milkman has 48 litres of mixture of milk and water in the ratio 5 : 1, respectively. He withdraws some amount of the mixture from the vessel and replaces it with milk. The ratio of the mixture of milk and water now becomes 7 : 1. What amount of the mixture is withdrawn?
Explanation
Capacity = 48 litres
Amount of milk = 5/6 x 48 = 40 litres
Amount of water =1/6 x 48 = 8 litres
Let the amount withdrawn be x.
Thus,
⇒ x = 12 litres
Question for Practice Questions Level 2: Mixtures & Alligations - 1
Try yourself:Puneet bought a mobile and a computer. Then he sold these to his friend Manjeet. He made a loss of 10% on the mobile and an overall profit of 15%. If the ratio of the costs of mobile and computer was 2 : 5, what was the profit made on the computer?
Explanation
By the rule of Alligation,
⇒ 5x - 75 = 50
⇒ 5x = 125
⇒ x = 25
Profit made on the computer = 25%
Question for Practice Questions Level 2: Mixtures & Alligations - 1
Try yourself:How many litres of a 77% solution of alcohol must be added to 20 litres of a 65% alcoholic drink to obtain a 68% alcoholic drink?
Explanation
Let the amount of solution having 77% solution of alcohol be x litres.
Now, apply the alligation formula.
Question for Practice Questions Level 2: Mixtures & Alligations - 1
Try yourself:The ratios of spirit to wine in two flasks labelled as A and B, containing spirit and wine mixture, are 7 : 3 and 3 : 1, respectively. Some amounts of the mixtures from the two flasks are poured into a third flask. The new mixture now contains spirit and wine in the ratio of 11 : 4. Find the ratio in which the mixtures from the flask A and flask B are mixed together to get this new mixture.
Question for Practice Questions Level 2: Mixtures & Alligations - 1
Try yourself:A sum of Rs. 39,00,000 is allotted for providing compensation to the victims of a train accident. The authorities have decided to sanction an amount of Rs. 30,000 to the injured and Rs. 80,000 to the families of the dead passengers. If there are total 65 victims, then find the number of injured passengers.
Question for Practice Questions Level 2: Mixtures & Alligations - 1
Try yourself:One alloy contains 90% copper and 10% tin. Another alloy contains 93% copper and 4% tin. If they are mixed so that the mixture may contain 9% of tin, then what percent of copper will it contain?