TCS NQT Allegations and Mixtures Questions Quiz 1

the concentration is given which is wrt 100, hence we can take x lt of 90% and (30-x)of 75%

x*90 + (30-x)*75 = 30*78

hence the ans is 6 liters.



Video solution:

Assume that a container contains x of liquid from which y units are taken out and replaced by water. After n operations, the quantity of pure liquid

x\left ( 1-\frac{y}{x} \right )^{n}

Hence juice in the jar = 30\left ( 1-\frac{3}{30} \right )^{3}

=> 30\left ( 1-\frac{1}{10} \right )^{3} = 21.87 litres



Video solution:

Wheat worth Rs. 124 per kg and Rs. 130 per kg are mixed in the ratio 1 : 1

So their average price = (124+130)/2=127

Hence let’s consider that the mixture is formed by mixing two varieties of wheat, one at Rs. 127 per kg and the other at Rs. x per kg in the ratio of 1:1

Cost of 1 kg of 1st kind                              Cost of 1 kg tea of 2nd kind

            Rs. 127                                                                  Rs. x

                                                Mean Price

                                                   Rs. 150

             (x-150)                                                                    23

 

\frac{(x-150)}{23} = 1

x= Rs 173



Video solution:

Let the actual amount of A be 4x and actual amount of B be 3x since A and B are in the ratio 4/3

amount of first basic element in the new alloy T (5/8)*4x + (1/3)*3x = (7x)/2

amount of second basic element in the new alloy T (3/8)*4x + (2/3)*3x= (7x)/2

so ratio of first basic element to second basic element: [(7x)/2 ] / [ 7x/2] = 1/1 = 1:1 ( Answer A)



Video solution:

Final quantity = initial quantity(1-(removed quantity/total)^no of times repeated

= 729(1-(n/729))⁶



Video solution:

Percentage of milk in first mixture

= [5/6] x 100 = 250/3 %

Percentage of milk in second mixture

= [7/9] x 100 = 700/9

Using Alligation method,



So, Required Ratio = [20/9] : [10/3] = 2:3



Video solution:

Let the quantity of mixture be X Liters

The cost of 1 L milk is = Rs 1.08 = 108 Paise

We have,

(X + 16) * 90 = (X * 108) + (16 * 0) (as cost of water is Zero)

90X + 16*90 = 108X

16 * 90 = 18X

X = (16 * 90)/18

X = 8 * 10

X = 80 L



Video solution:

Given 25 liters of sol has 20% sugar .
qty of sugar =(20%/100%)*25 =5 lit of sugar
(assume sugar qty in liter for easy calculation ).
therefore 25 lit sol contain 20 lit of water and 5 liter of sugar .
now the sol boils losing 10 liter of water .
therefore the new 15 liter sol contains 10 liter water and 5 liter sugar . there new % of sugar is 5/15 * 100 =33.33%



Video solution:

Consider 90 litre of solution1 and 60 litre of solution2

90 litre of solution1 contains 90*1/5=18 litre of milk and (90-18)=72 litre of water
60 litre of solution2 contains 60*1/3=20 litre of milk and (60-20)=40 litre of water

Mixture will have 18+20=38 litre of milk 72+40=112 litre of water
i.e., Quantity of milk : Quantity of water = 38 : 112 = 19 : 56

Take 75 litre of solution1. Quantity of milk = 75*1/5=15 litre. Profit earned in selling solution is 20%
assume cost price of 1 litre of milk = Rs.1
Cost price of 75 litre of solution1 = Rs.15.
Selling price of 75 litre of solution1 = 15*120/100 = Rs.18

Take 75 litre of mixture. Quantity of milk = 75*19/75=19 litre.
Cost price is Rs.19
Selling price will be same and is Rs.18
so there will be a loss
Loss = Rs.1 in selling 75 litre of the mixture
Percentage loss = 1*100/19 = 5.25% loss