ALLIGATION - 1st part

1. (i) In what proportion must rice at Rs. 3.10 per kg. be mixed with rice at Rs 3.60 per kg. so that the mixture be worth Rs. 3.25 a kg.?  [Ans. (c) 7 : 3]

(a) 3 : 7   (b) 5 : 3      (c) 7 :        (d) 7 : 13       (e) none of these

(ii) In what proportion must rice at Rs. 3.20 per kg. be mixed with rice at Rs 3.70 per kg. so that the mixture be worth Rs. 3.35 a kg.?   [Ans. (a) 7 : 3]

(a) 7 : 3    (b) 7 : 5     (c) 1 : 3  (d) 3 : 7    (e) none of these

(iii) In what proportion must coffee at Rs. 21 per kg. be mixed with coffee at Rs 28 per kg, so that the mixture be worth Rs. 25 a kg.?  [Ans. (d) 3 : 4]

(a) 4 : 3    (b) 4 : 5   (c) 1 : 3       (d) 3 : 4   (e) none of these

2. (i) A jar full of whisky contains 40% of alcohol. A part of this whisky is replaced by another containing 19% alcohol and now the percentage of alcohol was found to be 26. The quantity of whisky replaced is :  [Ans. (c) 2/3]    

(a)  1/3      (b)  3/5     (c)  2/3  (d) 2/5   (e) none of these

(ii) A jar full of whisky contains 65% of alcohol. A part of this whisky is replaced by another containing 30% alcohol and now the percentage of alcohol was found to be 51. The quantity of whisky replaced is :  [Ans. (a) 2/5]    

(a)  2/5  (b)  3/2   (c)  5/3    (d) 3/5   (e) none of these

3. (i) A mixture of a certain quantity of milk with 16 litres of water is worth 90P per litre. If pure milk be worth 108 P per litre how much milk is there in the mixture? [Ans. (a)  80 ]

(a)  80 liters  (b)  60 liter   (c) 90 liters (d)  75 liters  (e) none

(ii) A mixture of a certain quantity of milk with 25 litres of water is worth Rs.2 per litre. If pure milk be worth Rs. 12 per litre, how much milk is there in the mixture? [Ans. (c) 5 liters]   

(a)  2 liters (b) 10 liters   (c) 5 liters (d) 6 liters  (e) none

(iii) A mixture of a certain quantity of milk with 32 litres  of water is worth Rs.1.50 per litre. If pure milk be worth Rs. 4.50 per litre, how much milk is there in the mixture?  [Ans. (e) none of these (16 liters)]   

(a)  12 liters   (b)  20 liters  (c)  15 liters   (d)  26 liter (e) none

4. (i) A solution of sugar syrup has 15% sugar. Another solution has 5% sugar. How many litres of the second solution must be added to 20 litres of the first solution to make a solution of 10% sugar?  [Ans. (c) 20 litres]   

(a)  15 litres  (b)  30 litres  (c) 20 litres  (d)  25 litres   (e) none

5. (i) How much water must be added to a cask which contains 40 litres of milk at cost price Rs 3.5/litre so that that cost of milk reduces to Rs 2/litre ?    [Ans. (c) 30 litres]   

(a)  45 litres  (b)  20 litres  (c) 30 litres  (d)  25 litres    (e) none

(ii) How much chicory at Rs 24 a kg should be added to 15 kg of tea at Rs. 60 a kg., so as to make the mixture worth Rs. 39 a kg. ?  [Ans. (c) 21 kg.]   

(a)  20 kg.  (b)  25 kg.   (c)  21 kg.       (d)   31 kg.    (e) none

6. (i) A trader has 50 kg of pulses, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. What is the quantity sold at 18% profit ?   [Ans. (d) 30 kg.]

(a)  20 kg.    (b)  40 kg.    (c)  35 kg.    (d)  30 kg.         (e) none

(ii) A trader has 50 kg of pulses, part of which he sells at 10% profit and the rest at 5% loss. He gains 7% on the whole. What is the quantity sold at 5% loss ?  [Ans. (a) 10 kg.]

(a)  10 kg.    (b)  5 kg.    (c)  45 kg.    (d)  30 kg.  (e) none

(iii) A trader has 50 kg of pulses, part of which he sells at 14% profit and the rest at 6% loss. He losses 4% on the whole. What is the quantity sold at 6% loss ?   [Ans. (d) 45 kg.]

(a)  5 kg.   (b)  40 kg  (c)  35 kg.    (d)  45 kg.       (e) none

7. (i) There are 65 students in a class, 39 rupees are distributed among them so that each boy gets 80 P and each girl gets 30 P. Find the number of boys and girls in that class         [Ans. (c)]

(a) 34, 24   (b) 32, 24  (c) 39, 26  (d) 24, 34   (e) none of these

(ii) There are 60 students in a class, 40 rupees are distributed among them so that each boys gets 90 P and each girl gets 45 P. Find the ratio of boys  to the girls? [Ans. (a) 13 : 14]

(a) 13 : 14   (b) 12 :13   (c) 14 : 13 (d) 13 : 12   (e) none

(iii) There are 50 students in a class, 32 rupees are distributed among them so that each boys gets Re 1 and each girl gets 50 P. Find the number of boys in that class ?  [Ans. (e) of these]

(a)  24     (b)  32    (c)  20      (d)  36    (e) none of these

8. (i) 300 gm of sugar solution has 40% sugar in it. How much sugar should be added to make it 50% in the solution?  [Ans. (a) 60 gm]   

(a)  60 gm    (b) 65 gm    (c)   50 gm  (d)   55 gm      (e) none

(ii) A petrol pump owner mixed leaded and unleaded petrol in such a way that the mixture contains 10% unleaded petrol. What quantity of leaded petrol should be added to 1 litre mixture so that the percentage of unleaded petrol becomes 5%.  [Ans. (b) 1000 ml]   

 (a) 900 ml   (b) 1000 ml (c) 1900 ml  (d)   1800 ml     (e) none

(iii) 729 ml of a mixture contains milk and water in the ratio 7 : 2. How much more water is to be added to get a new mixture containing milk and water in ratio 7 : 3 ?  [Ans. (e) none of these {81 ml}]   

(a) 600 ml  (b) 710 ml  (c) 520 ml  (d) 810 ml      (e) none

(iv) In a mixture of 60 litres, the ratio of milk and water is 2 : 1. If the ratio of milk and water is 1 : 2, then the amount of water to be further added is : [Ans. (a)  60 litres]    

(a) 60 litre (b) 65 litres  (c) 50 liters    (d) 40 litres       (e) none

(v) A mixture of 66 litres of milk and water are in the ratio 5 : 1, and water is added to make the ration 5 : 3. Find the quantity of water added.  [Ans. (d)  22 ]   

(a) 24 litres (b) 18 liters  (c) 20 litres  (d) 22 liters      (e) none

(vi) 15 liters of a mixture contains 20% alcohol and the rest water. If 3 liters of water be mixed in it, the percentage of alcohol in the new mixture will be : [Ans. (c) 16&2/3%]   

(a) 17%     (b) 18.5%    (c) 16&2/3%    (d) 15%     (e) none

(vii) In a 30-litre mixture of water and alcohol, there is 90% alcohol. What amount of water should be mixed in the mixture so that the alcohol content becomes 80%? [Ans. (d) 3.75 liters]

(a)  3.5 liters(b) 2.75 liters(c)  6.5 liters (d) 3.75 liters (e)  none

(viii) Milk contains 5% water. What quantity of pure milk should be added to 10 liters of milk to reduce this to 2%? [Ans. (c)15 liters]

(a)  5 liters    (b) 7 liters     (c)  15 liters    (d)Can’t be determined (e)  none of these

(ix) The wheat sold by a grocer contained 10% low-quality wheat. What quantity of good-quality wheat should be added to 150 kg of wheat so that the percentage of low-quality wheat becomes 5%?  [Ans. (a) 150.]

(a)  150 kg. (b)  135 kg.   (c)  50 kg.  (d)  85 kg.       (e)  none

9. (i) A person travels 285 km in 6 hours in two stages. In the first part of the journey, he travels by bus at the speed of 40 km per hour. In the second part of the journey, he travels by train at the speed of 55 km per hr. How much distance did he travel by train ?  [Ans. (c) 165 km]

(a) 142.5 km   (b) 180 km  (c) 165 km   (d) 120 km     (e) none

(ii) A person travels 255 km in 7 hours in two stages. In the first part of the journey, he travels by bus at the speed of 30 km per hour. In the second part of the journey, he travels by train at the speed of 45 km per hr. How much distance did he travel by bus? [Ans. (d) 120 km]

(a) 125 km (b) 135 km   (c) 145 km   (d) 120 km       (e) none

10. (i) A vessel of 80 liters is filled with milk and water. 70% of milk and 30% of water is taken out of the vessel. It is found that the vessel is vacated by 55%. Find the initial quantity of milk.   [Ans. (a) 50 liters]   

(a)  30 liters  (b)  60 liters  (c) 10 liters  (d)  25 liters    (e) none

(ii) A vessel of 120 liters is filled with milk and water. 80% of milk and 40% of water is taken out of the vessel. It is found that the vessel is vacated by 65%. What is the ratio of milk and water ?  [Ans. (c) 5 : 3]   

(a)  6 : 5    (b)  3 : 5     (c)  5 : 3    (d)  4 : 3    (e) none of these

11. (i) In a zoo, there are rabbits and pigeons. If heads are counted, there are 200 and i legs are counted, there are 580. How many pigeons are there?   [Ans. (a) 110]   

(a) 110     (b)  90      (c)  120    (d)  150        (e) none of these

(ii) In a zoo, there are rabbits and pigeons. If heads are counted, there are 100 and if legs are counted, there are 290. How many rabbits are there ?   [Ans. (b) 45]   

(a) 100          (b)  45    (c)  50     (d)  55     (e) none of these

(iii) In a courtyard there are many chickens and goats. If heads are counted, it comes to 100, but when legs are counted, it comes to 320. Find the number of chickens and goats in the courtyard.  [Ans. (b) 40, 60]   

(a)  50, 50 (b)  40, 60  (c)  60, 40   (d)  55, 45 (e) none of these

12. (i) A container contains 7 parts of milk and 3 parts of water. How many parts of mixture should be taken out and replaced by water so that container contains half milk and half water   [Ans. (a) 2/7]    

(a)  2/7    (b)  3/5     (c)  5/7     (d) 2/5      (e) none of these

(ii) A container contains 8 parts milk and 4 parts water. How many parts of mixture should be taken out and replaced by water so that container contains half milk and half water.  [Ans. (d) 1/4]    

(a)  2/7     (b)  3/4      (c)  5/7       (d) 1/4    (e) none of these

13. (i) One type of liquid contains 25% of milk, the other contains 30% of milk. A can is filled with 6 parts of the first liquid and 4 parts of the second liquid. Find the percentage of milk in the new mixture.   [Ans.(d) 27%]    

(a)  30%    (b) 25%    (c) 32%        (d) 27%     (e) none of these

(ii) One type of liquid contains 12.5% of milk, the other contains 15% of milk. A can is filled with 8 parts of the first liquid and 12 parts of the second liquid. Find the percentage of milk in the new mixture   [Ans. (d) 14%]    

(a)  10%    (b)  15%   (c)  22%    (d)   14%  (e) none of these

14. (i) A man mixes 5 kilolitres of milk at Rs.600 per kilolitre with 6 kilolitres at Rs.540 per kilolitre. How many kilolitres of water should be added to make the average value of the mixture Rs.480 per kilolitre?  [Ans. (a) 2 kilo liters]

(a)  2          (b)  3          ) 1           d) 2.5         (e) none of these

(ii) A man mixes 6 kilolitres of milk at Rs.650 per kilolitre with 7 kilolitres at Rs.600 per kilolitre. How many kilolitres of water should be added to make the average value of the mixture Rs.540 per kilolitre  [Ans. (b) 2 kilo litres]

 (a)  3 kilolitres (b) 2 kilolitres(c) 1 kilolitre (d) 2.5 kilolitres         

15. (i) If 2 kg. of metal, of which 1/3 is zinc and the rest of copper, be mixed with 3 kg of metal, of which 1/4 is zinc and the rest is  copper, what is the ratio of  zinc to copper? [Ans. (b) 17 : 43]   

(a) 7 : 53  (b)  17 : 43  (c)19 : 41  (d)data inadequate (e) none

(ii) If 1 kg. of metal, of which 1/3 is zinc and the rest of copper, be mixed with 2 kg of metal, of which 1/4 is zinc and the rest is  copper, what is the ratio of  zinc to copper ?  [Ans. (b) 5 : 13]   

(a)  7 : 3   (b)  5 : 13 (c) 11 : 7   (d) data inadequate     (e) none