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.

Given:

A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup.

Explanation:

3 parts water and 5 parts syrup.

So water = 3/8 and syrup = 5/8

To make them equal,

Skill Academy

4/8 of water and syrup should be there

Let x be the amount of liquid we replace by water,

Water = 3x/8 and Syrup = 5x/8

Now,

Water before replacement + 5x/8= syrup before replacement - 5x/8

=> syrup-water(before replacement) = 10x/8 5x/4

=> 5/8 part-3/8 part = 5x/4

=>1/4 part = 5x/4

⇒x=1/5

So, 1/5 of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup.

Let P unit of the first mixture is added to Q unit of the second mixture.
So, in P unit of first mixture,
Amount of milk present = 5/7 * P = 5P/7
Amount of water present = 2/7 * P = 2P/7
So, in Q unit of second mixture,
Amount of milk present = 7/13 * Q = 7Q/13
Amount of water present = 6/13 * Q = 5Q/13
According to the question,
(5P/7 + 7Q/13) ÷ (2P/7 + 6Q/13) = 8/5
→ \frac{(33P + 30Q)}{55} : \frac{(22P+ 25Q)}{55} = 8/5
⇒ 325P + 245Q = 208P + 336Q
⇒ 117P = 91Q
⇒P: Q = 91:117 = 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