Answer: Option C
Explanation:
By the rule of alligation:
Cost of 1 kg pulses of 1^{st} kindCost of 1 kg pulses of 2^{nd} kind 
Rs. 15  Mean Price Rs. 16.50  Rs. 20 
3.50  1.50 
Required rate = 3.50 : 1.50 = 7 : 3.
6. 
A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25%. The percentage of water in the mixture is:

Answer: Option C
Explanation:

7. 
How many kilogram of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per kg so that there may be a gain of 10% by selling the mixture at Rs. 9.24 per kg?

Answer: Option D
Explanation:
S.P. of 1 kg of mixture = Rs. 9.24, Gain 10%.
C.P. of 1 kg of mixture = Rs.   100  x 9.24   = Rs. 8.40 
110 
By the rule of allilation, we have:
C.P. of 1 kg sugar of 1^{st} kindCost of 1 kg sugar of 2^{nd} kind 
Rs. 9  Mean Price Rs. 8.40  Rs. 7 
1.40  0.60 
Ratio of quantities of 1 ^{st} and 2 ^{nd} kind = 14 : 6 = 7 : 3.
Let x kg of sugar of 1^{st} be mixed with 27 kg of 2^{nd} kind.
Then, 7 : 3 = x : 27

8. 
A container contains 40 litres of milk. From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?

A.  26.34 litres 
B.  27.36 litres 
C.  28 litres 
D.  29.16 litres 

9. 
A jar full of whisky contains 40% 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:

Answer: Option B
Explanation:
By the rule of alligation, we have:
Strength of first jarStrength of 2^{nd} jar 
40%  Mean Strength 26%  19% 
7  14 
So, ratio of 1^{st} and 2^{nd} quantities = 7 : 14 = 1 : 2
Required quantity replaced =  2 
3 

10. 
In what ratio must water be mixed with milk to gain 16 % on selling the mixture at cost price?

Answer: Option 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  x 1   =  6 
350  7 
By the rule of alligation, we have:
C.P. of 1 litre of waterC.P. of 1 litre of milk 
0  Mean Price
 Re. 1 


Ratio of water and milk =  1  :  6  = 1 : 6. 
7  7

1. 
Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg.

Answer: Option B
Explanation:
By the rule of alligation:
Cost of 1 kg of 1^{st} kindCost of 1 kg of 2^{nd} kind 
720 p  Mean Price 630 p  570 p 
60  90 
Required ratio = 60 : 90 = 2 : 3.

12. 
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%?

Answer: Option 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  x 68.20   = Rs. 62. 
110 
By the rule of alligation, we have:
Cost of 1 kg tea of 1^{st} kind.Cost of 1 kg tea of 2^{nd} kind. 
Rs. 60  Mean Price Rs. 62  Rs. 65 
3  2 
Required ratio = 3 : 2.

13. 
The cost of Type 1 rice is Rs. 15 per kg and Type 2 rice is Rs. 20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is:

A.  Rs. 18 
B.  Rs. 18.50 
C.  Rs. 19 
D.  Rs. 19.50 
Answer: Option A
Explanation:
Let the price of the mixed variety be Rs. x per kg.
By rule of alligation, we have:
Cost of 1 kg of Type 1 riceCost of 1 kg of Type 2 rice 
Rs. 15  Mean Price Rs. x  Rs. 20 
(20  x)  (x  15) 
 (20  x)  =  2 
(x  15)  3 
60  3 x = 2 x  30
5 x = 90
x = 18.

14. 
8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of water is 16 : 65. How much wine did the cask hold originally?

A.  18 litres 
B.  24 litres 
C.  32 litres 
D.  42 litres 
Answer: Option B
Explanation:
Let the quantity of the wine in the cask originally be x litres.
Then, quantity of wine left in cask after 4 operations =   x   1   8   4  litres. 
x 
3 x  24 = 2 x
x = 24.

15. 
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:

Answer: Option C
Explanation:
By the rule of allegation, we have:
Profit on 1^{st} partProfit on 2^{nd} part 
8%  Mean Profit 14%  18% 
4  6 
Ration of 1^{st} and 2^{nd} parts = 4 : 6 = 2 : 3
Quantity of 2^{nd} kind =   3  x 1000  kg  = 600 kg. 
5 



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