Average, Mixture, and Alligation








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Quiz Begins Here

Q #1
:

Directions: Refer the following data to answer the questions given below.

The milk and water in two vessels A and B are in the ratio 4:3 and 2:3 respectively. In what ratio the liquids in both the vessels be mixed to obtain a new mixture in vessel c consisting half milk and half water?

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Milk in 1 litre mixture of A = 4/7 litre.
Milk in 1 litre mixture of B = 2/5 litre.
Milk in 1 litre mixture of C = 1/2 litre.


By rule of alligation we have required ratio X:Y

Q #2
:

Directions: Refer the following data to answer the questions given below.

Two vessels A and B contain spirit and water mixed in the ratio 5:2 and 7:6 respectively. Find the ratio in which these mixture be mixed to obtain a new mixture in vessel c containing spirit and water in the ratio 8:5?

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Spirit in 1 litre mix of A = 5/7 litre.
Spirit in 1 litre mix of B = 7/13 litre.
Spirit in 1 litre mix of C = 8/13 litre.
By rule of alligation we have required ratio X:Y

Q #3
:

Directions: Refer the following data to answer the questions given below.

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

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Let the rate of second quality be Rs x per Kg.

C.P of 1Kg wheat of 1st 980p 

Step 1 : 

S.P of 1 kg of mixture = Rs. 9.24

Gain = 10%

C.P of 1 kg of mixture =[100/100+10×9.24]=Rs.8.40

Mean price = Rs. 8.40

Step 2 : 

C.P of  1 kg of sugar of  1st kind = 900p

C.P of  1 kg of sugar of  2nd kind = 700p

Mean price = 840p


Q #4
:

Directions: Refer the following data to answer the questions given below.

One quantity of wheat at Rs 9.30 per Kg is mixed with another quality at a certain rate in the ratio 8:7. If the mixture so formed be worth Rs 10 per Kg, what is the rate per Kg of the second quality of wheat?

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Let the rate of second quality be Rs x per Kg.

C.P of 1Kg wheat of 1st kind = 930p 

C.P of 1 Kg wheat of 2nd kind = 100x p 

Mean price = 1000p

By rule of alligation we have required ratio 8 : 7


Q #5
:

Directions: Refer the following data to answer the questions given below.

A can contains a mixture of two liquids A and B in the ratio 7:5 when 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many litres of liquid A was contained by the can initially?

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Suppose the can initially contains 7x and 5x litres of mixtures A and B respectively.

When 9 litres of mixture are drawn off, quantity of A in mixture left:

7x–(7/12)×9=7x−21/4 litres

Similarly quantity of B in mixture left:

5x−(5/12)×9=5x−(15/4) litres

Therefore ratio becomes:

7x–(21/4)/5x−(15/4)+9=7/9

(28x−21)/(20x+21)=7/9

(252x−189)=140x+147 

112x=336 

x=3

 So the can contained:  7×x=7×3= 21 litres of A initially