Cognizant Allegation & Mixtures Quiz-1

Since first second varieties are mixed in equal proportions, so their average price = Rs.(126+135)/2= Rs.130.50

So, Now the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say Rs. 'x' per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find 'x'.

Rs.130.50                           Rs.x

Rs.15

Rs. (x-153)                         Rs.22.50

x-153/22.50 = 1 => x - 153 = 22.50 => x=175.50.

Hence, price of the third variety = Rs.175.50 per kg.

Video solution:

Let the quantity of the wine in the cask originally be x litres. 8 litres of wine is removed from it and replaced with water. This operation is done total 4 times. After 4 operation,

Wine : Water = 16 : 65 or Wine : Total = 16 : 81

[(x-8)/x]⁴ = 16/81

(x-8)/x = 2/3

3x - 24 = 2x

x = 24

Explanation:

“/” sign is missing in explanation

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

Quantity of A in mixture left ={7x−(7/12)×9}=(7x−21/4)7x-712×9=7x-21/4 litres.

Quantity of B in mixture left =  (5x−512×9)=(5x−15/4)5x-512×9=5x-15/4litres.

 

(7x−21/4)(5x−15/4)+9=797x-2145x-154+9=79

⇒28x−2120x+21=79⇒28x-2120x+21=79

⇒x=3⇒x=3

So, the can contained 21 litres of A.

 

We will consider 10 parts of liquid A and 4 parts of liquid B with each part a unit volume. For ease of understanding, the unit can even be taken as a liter. Unit can be any because all values, given and desired, are in percentages that are basically ratios of two values (so that units cancel out).

With this understanding, we will calculate the amount of water in each of 10 parts or 10 liters of liquid A and 4 parts or 4 liters of liquid B.

Let the C.P of spirit be = Rs.10 per litre

Then S.P l litre of the mixture = Rs. 11

Profit = 20%

Therefore, C.P of the mixture =  Rs[(100/120)*10]=Rs. 25/3 per litre

Explanation:

Number of liters of water in 125 liters of the mixture = 20% of 150 = 1/5 of 150 = 30 liters

Let us Assume that another \'P\' liters of water are added to the mixture to make water 25% of the new mixture. So, the total amount of water becomes (30 + P) and the total volume of the mixture becomes (150 + P)

Thus, (30 + P) = 25% of (150 + P)

Solving, we get P = 10 liters

Video solution:

Let his expenditure and savings be $30$ and $20$ respectively.
Then his income is $30+20=50$

New income $=\frac{50\times \mathrm{115/}}{100}=57.5$
New savings $=\frac{20\times \mathrm{106/}}{100}=21.20$
New expenditure $=57.5-21.20=36.3$

Percentage increase in expenditure $=\frac{(36.3-30)\times 100}{30}=21\%$

Video solution:

Explanation:

Let the price of the mixed variety be Rs. x per kg. By the rule of alligation, we have :

Cost of 1 kg of type 1 rice           Cost of 1 kg of type 2 rice



(20-x)/(x-15) = 2/3

⇒⇒ 60 - 3x = 2x - 30

⇒⇒ x = 18.

Video solution:

Suppose the vessel initially contains 8 liters of liquid.

Let x liters of this liquid be replaced with water.
Quantity of water in new mixture = (3− 3x/8 +x)liters.

Quantity of syrup in new mixture = (5−5x/8) liters.
(3− 3x/8 + x)=(5− 5x/8)
=> 5x + 24 = 40 - 5x
=> 10x = 16 => x = 8/5
So, part of the mixture replaced = (8/5 × 1/8) = 1/5.

Video solution:

 

Explanation:

By the rule of alligation:

C.P. of 1 kg sugar of 1st kind      C.P. of 1 kg sugar of 2nd kind

Therefore, Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3.



Let x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind.

Then, 7 : 3 = x : 27 or x = (7 x 27 / 3) = 63 kg.