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1.
A merchant has 1000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is:
  • A.
    400 kg
  • C.
    600 kg
  • B.
    650 kg
  • D.
    640 kg
  • Answer & Explanation
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Answer : [C]
Explanation :
 
By the rule of alligation, we have :
 
  Profit on 1st part Profit on 2nd part  
8%
 
4
 
 
 
Mean Profit
14%
 
 
18%
 
6
 
Ratio of 1st and 2nd parts = 4 : 6 = 2 : 3
 
 
  Quantity of 2nd kind =  
3
5
 x 1000    kg = 600 kg.  
 
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2.
Two vessels A and B contain milk and water mixed in the ratio 8 : 5 and 5 : 2 respectively. The
ratio in which these two mixtures be mixed to get a new mixture containing 69
3
13
% milk, is:
  • A.
    2 : 7
  • C.
    5 : 2
  • B.
    3 : 5
  • D.
    5 : 7
  • Answer & Explanation
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Answer : [A]
Explanation :
 
Let cost of 1 litre milk be Re. 1.
 
Milk in 1 litre mix. in A =
8
13
 litre; C.P. of 1 litre mix. in A = Re.
8
13
   
 
Milk in 1 litre mix. in B =
5
7
 litre; C.P. of 1 litre mix. in B = Re.
5
7
   
 
Milk in 1 litre of final mix. =  
900
13
x
1
100
x 1   =
9
13
 litre; Mean price = Re.
9
13
 
 
By the rule of alligation, we have :
 
  C.P. of 1 litre mixture in A C.P. of 1 litre mixture in B  
8
13
 
2
91
 
 
Mean Price
9
13
 
 
5
7
 
1
13
 
 
  Required ratio =
2
91
:
1
13
 = 2 : 7.  
 
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3.
In what ratio must a grocer mix two varieties of tea worth Rs. 60 a kg and Rs. 65 a kg so that by selling the mixture at Rs. 68.20 a kg he may gain 10%?
  • A.
    3 : 2
  • C.
    3 : 5
  • B.
    3 : 4
  • D.
    4 : 5
  • Answer & Explanation
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Answer : [A]
Explanation :
 
S.P. of 1 kg of the mixture = Rs. 68.20, Gain = 10%.
 
C.P. of 1 kg of the mixture = Rs.  
100
110
x 68.20    Rs. 62  
 
BY the rule of alligation, we have :
 
  Cost of 1 kg tea of 1st kind Cost of 1 kg tea of 2nd kind  
Rs. 60
 
3
 
 
 
Mean Price
Rs. 62
 
 
Rs. 65
 
2
 
 
  Required ratio = 3 : 2.  
 
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4.
In what ratio must tea Rs. 62 per kg be mixed with tea at Rs. 72 per kg so that the mixture must be worth Rs. 64.50 per kg?
  • A.
    3 : 1
  • C.
    4 : 3
  • B.
    3 : 2
  • D.
    5 : 3
  • Answer & Explanation
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Answer : [A]
Explanation :
 
By the rule of alligation:
 
  Cost of 1 kg tea of 1st kind Cost of 1 kg tea of 2nd kind  
6200 p
 
750
 
 
 
Mean Price
6450 p
 
 
7200 p
 
250
 
 
  Required rate = 750 : 250 = 3 : 1  
 
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5.
In what ratio must water be mixed with milk to gain 16
2
3
% on selling the mixture at cost    
price?
  • A.
    1 : 6
  • C.
    2 : 3
  • B.
    6 : 1
  • D.
    4 : 3
  • Answer & Explanation
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Answer : [A]
Explanation :
 
Let C.P. of 1 litre milk be Re. 1.
 
S.P. of 1 litre of mixture = Re. 1, Gain =
50
3
%    
 
 
  C.P. of 1 litre of mixture =   100 x
3
350
x 1    = Re.
6
7
 
 
By the rule of alligation, we have :
 
  C.P. of 1 litre of water C.P. of 1 litre of milk  
0
 
1
7
 
 
Mean Price
  Re.
6
7
 
 
 
Re. 1
 
6
7
 
 
  Ratio of water and milk =
1
7
:
6
7
 = 1 : 6  
 
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