Allegations and Mixtures Quiz 1

Number of liters of water in100 liters of the mixture = 20% of 100 = 20/100 * 100 = 20 liters.

P liters of water added to the mixture to make water 25% of the new mixture.

The total amount of water becomes (20 + P) and the total volume of the mixture is (100 + P).

(20 + P) = 50/100 * (100 + P)

40 + 2P = 100 + P

=> P = 60 liters.

To find the ratio of apple cider vinegar and water in the final mixture

Apple cider vinegar = 3/5 * 20 = 12 liters, water = 8 liters

If 10 liters of the mixture are removed, the amount of apple cider vinegar removed = 6 liters and the amount of water removed = 4 liters.

Remaining apple cider vinegar = 12 - 6 = 6 liters

Remaining water = 8 - 4 = 4 liters

10 liters of pure apple cider vinegar are added, therefore total apple cider vinegar = (6 + 10) = 16 liters.

The ratio of apple cider vinegar and water in the new mixture = 16:4 = 4:1

If the process is repeated one more time and 10 liters of the mixture are removed, then amount of apple cider vinegar removed = 4/5 * 10 = 8 liters.

Amount of water removed = 2 liters.

Remaining Apple cider vinegar = (16 - 8) = 8 liters.

Remaining water = (4 -2) = 2 liters.

The required ratio of Apple cider vinegar and water in the final mixture obtained = (8 + 10):2 = 18:2 = 9:1.

 

Let the quantities of A and B mixed be 3y kg and 7y kg.

Cost of 3y kg of A = 10(3y) = Rs. 30y

Cost of 7y kg of B = 16(7y) = Rs. 112y

Cost of 10y kg of the mixture = 30y + 112y = Rs. 142y

Cost of 20 kg of the mixture = 142*2 = Rs. 284

Profit made in selling 20 kg of the mixture = 50/100 (cost of 20 kg of the mixture) = 50/100 * 284 = Rs. 142

Percentage of milk in the mixture formed = (\frac{\frac{(70)(150)}{100}+20}{150+20})\times 100% =(\frac{105+20}{170})\times 100 = (\frac{25}{34})\times 100% = 73.53%.

Let the capacity of the can be y liters.

Quantity of Balsamic Vinegar in the mixture before adding additional Balsamic Vinegar= \frac{4}{9} (y - 8)

After adding Balsamic Vinegar, the quantity of Balsamic Vinegar in the mixture = \frac{6}{11}y.

\frac{6y}{11}- 8 =\frac{4}{9}(y - 8)

10y = 792 - 352

=> y = 44.

Let us say the ratio of the quantities of cheaper and dearer varieties = x: y

By the rule of allegation, x/y = \frac{9-8}{8-7} = 1/1

Quantity of Balsamic Vinegar in vessel P = 62.5/100 * 2 = 5/4 litres

Quantity of Balsamic Vinegar in vessel Q = 87.5/100 * 4 = 7/2 litres

Quantity of Balsamic Vinegar in the mixture formed = 5/4 + 7/2 = 19/4 = 4.75 litres

As 6 litres of mixture is formed, ratio of Balsamic Vinegar and water in the mixture formed = 4.75 : 1.25 = 19 : 5.

Let the initial quantity of Sulfuric acid in the bottle be P liters.

Let us say y liters of the mixture is taken out and replaced by water for n times, alternatively.

Quantity of Sulfuric acid finally in the vessel is then given by \left ( \frac{p-y}{p} \right )^{n}\times p

For the given problem, P = 90, y = 9 and n = 2.

Hence, quantity of Sulfuric acid finally in the bottle

= \left ( \frac{90-9}{90} \right )^{2}\times 90

=  72.9 litres.

S.P of 1kg mix = RS.48.40, Gain = 10% C.P of 1kg mix =Rs.(100/110 x 48.40) =Rs.44

By using the rule of allegation:-

(Cheaper Tea) : (Dearer Tea) = I 54 - 44 I / I 49 - 44 I

= 2 : 1

Total cost price =Rs(250 x 30) = Rs.7500

Cost per litre =Rs.20,

Total quantity = 7500/20 = 375 Litres.

Water to be added =(375-250) =125 Litres.