Quiz – 1

% of Liquid in Solution A = 25%
⇒ % of Water in Solution A = 75%
Volume of Solution A = 24 Litres
⇒ Volume of Water in Solution A = (75/100) × 24 = 18 Litres
% of Liquid in Solution B = 30%
⇒ % of Water in Solution A = 70%
Volume of Solution B = 10 Litres
⇒ Volume of Water in Solution B = (70/100) × 10 = 7 Litres
If Solution A is mixed with Solution B
⇒ Net Total Volume of Solution = (24 + 10) = 34 Ltrs
⇒ Net Total Volume of Water in Solution = (18+ 7) = 25Ltrs
% of Water in New Mixture = (Volume of Water in New Mixture / Volume of New Mixture) × 100
% of Water in New Mixture = (25 /34) × 100 = 73.52%

let pure milk= x litr.
total mixture=x+4
3x*120/100=(x+4)3
6x-5x=20
x=20

ratio of water and milk remain same after sold of 40 ltr i.e 28/72
now remaining quantity is 165-40= 125
amount of water in 125 ltr is 125of 28%=35 ltr
amount of milk in 125 ltr= 125-35=90
now a/c to question 35+13/90+30=48/120
water amount is 48 ltr in total amount 125+30+13=168
hence the % of water is 48*100/168=28.57%

C.P of 1 Kg                   C.P of 1 Kg
rice of 1st                   rice of 2nd
kind (930p)                kind (1080p)
\\\\                        /
Mean Price
(1000p)
/                       \\\\
(1080 – 1000)  :        (1000 -  930)
80                             70

Thus, required ratio = 80 : 70 = 8 : 7

C.P of a unit quantity of 1st kind  = Rs. 3.20
C.P of a unit quantity of 2nd kind  = Rs. 2.90
Mean price = Rs.3.08
C.P of unit quantity         C.P of unit quantity
of 1st kind                         of 2nd kind
(Rs. 3.20)                         (Rs. 2.90)
\\\\                       /
Mean Price
(Rs.3.08)
/                        \\\\
(3.08 – 2.90)          :           (3.20 – 3.08)
0.18                                      0.12
Required ratio = 0.18 : 0.12 = 3 : 2

 

Milk in 1 litre mixture of A = 4/7 litre.
Milk in 1 litre mixture of B = 2/5 litre.
Milk in 1 litre mixture of C = 1/2 litre.
By rule of alligation we have required ratio X:Y
X                  :                 Y
4/7                                2/5
\\                      /
(Mean ratio)
(1/2)
/                      \\
(1/2 – 2/5)     :       (4/7 – 1/2)
1/10                      1/1 4
So Required ratio = X : Y = 1/10 : 1/14 = 7:5

Spirit in 1 litre mix of A = 5/7 litre.
Spirit in 1 litre mix of B = 7/13 litre.
Spirit in 1 litre mix of C = 8/13 litre.
By rule of alligation we have required ratio X:Y
X         :       Y
5/7              7/13
\\\\\\\\          /
(8/13)
/          \\\\\\\\
(1/13)     :     (9/91)
7                      9
Therefore required ratio = 1/13 : 9/91
= 7:9

Let the rate of second quality be Rs x per Kg.
C.P of 1Kg wheat of 1st kind = 930p
C.P of 1 Kg wheat of 2nd kind = 100x p
Mean price = 1000p
By rule of alligation we have required ratio 8 : 7
930                         x
\\\\\\\\                  /
(Mean Price)
(10)
/                  \\\\\\\\
x-10        :          0.7     ::       8        :          7
So we get required ratio,  (x-10) : 0.7 :: 8 : 7
⇒ x = 10.80 per Kg

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:

Profit (%) = 9.09 % = 1/11
Since the ratio of water and milk is  1 : 11,
Therefore the ratio of water is to mixture = 1:12
Thus the quantity of water in mixture of 1 liter = 1000 x (1/12) = 83.33 ml

Video solution: