Alligations and Mixtures Questions and Answers

As per the formula if two materials are mixed, then

\frac{\text{ Quantity of Cheaper }}{\text{ Quantity of Dearer }} = \frac{\text{ C.P of dearer - Mean Price }}{\text{ Mean Price - C.P. of cheaper }}

Let C.P. of 1 kg pulse be Re. 1

Then, Selling Price of 1 kg of mixture = Re. 1, Gain = 25%.

C.P of 1kg mixture = Re \frac{100}{125} \times 1 = \frac{4}{5}

By the rule of allegation, we have:

Ratio of pulse to pebble = \frac{4}{5} : \frac{1}{5} = 4: 1

Therefor, % of pebble in the mixture = \frac{1}{5} \times 100 \% = 20 \%

Amount of fresh juice left after 3 times = 100 \left( 1 - \frac{12}{100} \right) 3 times

= 100 \times \frac{22}{25} \times \frac{22}{25} \times \frac{22}{25} = 68.14 litres

Since first and second types are mixed in equal proportions.

So, their average price = Rs \frac{130 + 139}{2} = 134.50
So, the combination is made by mixing two types, one at Rs. 134.50 per kg and another one at INR x in the ratio 1 : 1. We have to find x.

As per the law of allegation:

\frac{x-163}{28.50} = 1

x-163=28.50

x=191.50

According to the rule of allegation:

Required rate = (21 - 18.50) : (18.50 - 14)

Price of second black-eyed peas-mean price: Mean price-cost of first black-eyed peas

2.50 : 4.50 = 5 : 9.

Let’s assume as volume of jug is 80 litres.

Water=30 litre

Tomato soup=50 litre

For every 8 litres taken out of the jug, we swap 5 litres of soup with water.

So, we need to exchange 16 litres with water.

Let the C.P. of coca cola be Re. 1 litre.
Coca cola in 1 litre mix. of X = 5/7 litre, C.P. of 1 litre mix.
In X = Re. 5/7
coca cola in 1 litre mix. of Y = 7/13 litre, C.P. of 1 litre mix.
in Y = Re. 7/13
coca cola in 1 litre mix. of Z = 8/13 litre, Mean price = Re. 8/13.

Required ratio = \frac{1}{13} : \frac{9}{91} = 7:9

Assume price of 1 litre petrol= INR 1

Selling price of 1 litre mix=1 rs.

Profit= 5/3percent

C.P. of 1 litre mix- \frac{100 \times 3}{350 \times 1}= \frac{6}{7}



Thus proportion of kerosene and petrol= \frac{1}{7} : \frac{6}{7} = 1:6

1 litre of water C.P. = Rs 0.

1 litre of Sangria C.P. = Rs 12.

Mean Price = Rs 8.

As per the Allegation formula: (Amount of Cheaper):(Amount of Dearer) = (CP of dearer - Mean Price):(Mean Price - CP of cheaper)

Therefore, Water: Sangria = (12-8):(8-0) = 4:8 = 1:2.

As per the allegation formula

=x(1−y/x)ⁿ=x(1−y/x)ⁿ units.

So, milk in the pot now =40(1−4/40)³=40(1−1/10)³ =29.16

Assume that the Third type of mustard seed quantity is X.

Then

\frac{(126 \times 3 + 135 \times 2 + 5 \times x)}{(3+2+5)}= 155

on solving
648 + 5x = 10 \times 155

5x = 1550-648
x=902/5
X= 180.40

Let x litres from 1^st pot and 12-x litres from 2^nd pot are mixed

Lemon water from 1^st pot = .75x

Soda from 1^st drum = .25x

Lemon water from 2^nd pot = .5(12-x)

Soda from 2^nd drum = .5(12-x)

Total lemon water = .25x+6

Total soda = .25x+.5(12-x) = 6-.25x

Proportion = \frac{(.25x+6)}{(6-.25x)} = \frac{5}{3} =.75x+18 = 30-1.25x

2x =12; x=6 lemon water and 6 soda

As given let x litres from 1^st tin and 12-x from 2^nd tin are mixed

Ghee from 1^st tin = .75x

Oil from 1^st tin = .25x

Ghee from 2^nd tin = .5(12-x); And oil from 2^nd drum = .5(12-x)

Total ghee = .25x+6

Total oil = .25x+.5(12-x) = 6-.25x

Proportion = \frac{(.25x+6)}{(6-.25x)} = \frac{5}{2}

0.50x+12 = 30-1.250x

1.75x= 18= 10.28 liters