Alligation or Mixture

Q 5: A zookeeper counted the heads of the animals in a zoo and found it to be 60. When he counted the legs of the animals he found it to be 280. If the zoo had either pigeons or horses, how many horses were there in the zoo? A)80 B)86 C)70 D)60 Answer : Option A Explanation: Let the number of horses =x Then the number of pigeons =60−x. Each pigeon has 2 legs and each horse has 4 legs. Therefore, total number of legs =4x+2(60−x)=280 ⇒4x+120−2x=280 ⇒2x=160 ⇒x=80. Q 6: The cost of Type 1 material is Rs. 10 per kg and Type 2 material is Rs.20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then what is the price per kg of the mixed variety of material? A) Rs.26 B) Rs.16 C) Rs.15 D) Rs.13 Answer : Option B Explanation: Cost Price(CP) of Type 1 material is Rs. 10 per kg Cost Price(CP) of Type 2 material is Rs. 20 per kg Type 1 and Type 2 are mixed in the ratio of 2 : 3. Hence Cost Price(CP) of the resultant mixture =(10Ũ2)+(20Ũ3)/(2+3)=(20+60)/5=80/5=16 Price per kg of the mixed variety of material = Rs.16 Q 7: In what ratio must a grocer mix two varieties of pulses costing Rs.12 and Rs. 20 per kg respectively to obtain a mixture worth Rs.16 per kg? A)2:1 B)1:1 C)1:2 D)1:3 Answer : Option B Explanation: By rule of alligation, CP of 1 kg of 1st variety pulse 12 CP of 1 kg of 2nd variety pulse 20 mean price 16 So, 16-12=4 and 20-16=4 Required Ratio = 4 : 4 = 1:1 Q 8: How many liters of water must be added to 12 liters of milk and water containing 20% water to make it 40% water in it? A)3 liters B)2 liters C)4 liters D)1 liters Answer : Option C Explanation: By rule of alligation, % Concentration of water in pure water (100) % Concentration of water in the given mixture (20) Mean % concentration (40) 100-40=60 and 40-20=20 => Quantity of water : Quantity of the mixture = 20 : 60 = 1 : 3 Here quantity of the mixture = 12 liters => Quantity of water : 12 = 1 : 3 => Quantity of water =12Ũ(1/3)=4 liters

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