Aptitude - Alligation or Mixture

Exercise :: Alligation or Mixture - General Questions

11. 

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.

A. 1 : 3
B. 2 : 3
C. 3 : 4
D. 4 : 5

Answer: Option B

Explanation:

By the rule of alligation:

Cost of 1 kg of 1st kind Cost of 1 kg of 2nd 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%?

A. 3 : 2
B. 3 : 4
C. 3 : 5
D. 4 : 5

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 1st kind. Cost of 1 kg tea of 2nd 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 rice Cost 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 - 3x = 2x - 30

5x = 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

x(1 - (8/x))4 = 16
x 81

1 - 8 4 = 2 4
x 3

x - 8 = 2
x 3

3x - 24 = 2x

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:

A. 400 kg
B. 560 kg
C. 600 kg
D. 640 kg

Answer: Option C

Explanation:

By the rule of alligation, we have:

Profit on 1st part Profit on 2nd part
8% Mean Profit
14%
18%
4 6

Ration of 1st and 2nd parts = 4 : 6 = 2 : 3

Quantity of 2nd kind = 3 x 1000 kg = 600 kg.
5


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