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Direction (1 – 5): Study the following information carefully and answer the given questions:

The given line graph shows the mixture of milk in the mixture of water and milk in 5 different vessel.

1) If the vessels-A, B and C, each of 400 liter capacity, then what is the ratio of milk and water in the resultant mixture, if all the three vessels mixture is poured into Jar?
a) 7:3
b) 3:5
c) 6:5
d) 5:4
e) None of these
2) There is 1000 liter of mixture in the vessel D. 200 liter of the mixture is taken out and same amount of water is poured into the vessel and again 400 liters of mixture is taken out and same amount of water is poured into vessel, then find the amount of milk in the resultant mixture?
a) 432 liter
b) 456 liter
c) 448 liter
d) 428 liter
e) None of these
3) The Vessel E of 120 liter of mixture of milk and water. 60% of milk and x% of the water is taken out of the vessel. If it is found that the vessels is vacated by 50%, and then find the value of x?
a) 40%
b) 30%
c) 20%
d) 10%
e) None of these
4) A vessel contains mixture of C, x part of the mixture should be withdrawn and replaced by water. If the ratio of the milk and water in the mixture will be 7:18, then find the value of x?
a) 8
b) 7
c) 6
d) Cannot be determined
e) None of these
5) Quantity I: In vessel A, 20 litres of mixture is taken out and 6 litres of water is added in the mixture, then the ratio of milk and water in the final mixture is 8: 3. Find the initial quantity of milk in the vessel
Quantity II: In vessel B, 15 litres of mixture is taken out and 3 litres of water is added in the mixture, then the ratio of water and milk in the final mixture is 7:9. Find the initial quantity of milk in the vessel
a) Quantity I > Quantity II
b) Quantity I < Quantity II
c) Quantity I ≥ Quantity II
d) Quantity I ≤ Quantity II
e) Quantity I = Quantity II (or) Relationship cannot be determined

Direction(6-10): Study the following table carefully and answer the question.

6). What is the respective ratio between total number of students who have enrolled for coaching institutes
A and C together from school P and total number of students who have enrolled for the same coaching
institutes together from school Q?
(a) 44:35 (b) 75:32 (c) 34:75 (d) 45:38 (e) None of these
7). In coaching institutes E, 40% are females. If 20% of the total females are from school Q, what is the
difference in number of Female students from school P, S and R who has enrolled from coaching institute
E to school Q?
(a) 18 (b) 40 (c) 13 (d) 35 (e) None of these
8). What is the average number of students have enrolled in coaching institutes A, C, E and D from school
P, R, Q, and S respectively?
(a) 45 (b) 61 (c) 51/2 (d) 23/2 (e) None of these
9). What percentage is the total number of students who have enrolled from coaching institute A from
schools P and S together and the total number of students who have enrolled for coaching institute C from
the same school together?
(a) 34.67% (b) 78.32% (c) 45.51% (d) 56.32% (e) None of these
10). In coaching institute B, the total number of students who have enrolled from schools P and R together
is what percent less than the total number of students from schools Q and S together?
(a)   72.41% (b) 45.23% (c) 27.58% (d) 40.23% (e) None of these
SOLUTION
Milk of vessel A=400*80/100=320 liter
Water of vessel A=400*20/100=80 liter
Milk of vessel B=400*60/100=240
Water of vessel B=400*40/100=160
Milk of vessel C=400*70/100=280
Water of vessel C=400*30/100=120
Required ratio = (320+240+280):(80+160+120)
=840:360
=7:3
Milk=1000*90/100=900 liter
Water=1000*10/100=100 liter
Ratio of the mixture=900:100=9:1
200 liters taken in the mixture,
Milk in remaining mixture = 800*9/10=720
Water in remaining mixture = 800*1/10=80,
Total water=80+200=280
Ratio=720:280=18:7
400 liters is taken out in the mixture, milk=600*18/25=432 liter
Milk=120*75/100=90 liter
Water=120*25/100=30 liter
60% of the milk=90*60/100=54 liter
Remaining milk=90*40/100=36 liter
Remaining water=30*(100-x)/100
Total mixture in the vessel now = (36+30-(3x/10)) = 66-3x/10
(66-3x/10)/120=50/100
(660-3x)/1200=50/100
660-3x=600
3x=60
X=20%
Ratio of mixture of milk to water=7:3 = 7y: 3y
(7y -(7/10*X))/(3y – 3/10x)+x=7/18
The given information is not sufficient to answer the given question. Because we don’t have any information about the initial quantity; instead, we only know the ratio of milk and water in the given mixture.
Quantity I: In vessel A, 20 litres of mixture is taken out and 6 litres of water is added in the mixture, then the ratio of milk and water in the final mixture is 8: 3. Find the initial quantity of milk in the vessel
Milk and water ratio = 80: 20
= 4: 1
Milk in the 20 litres of mixture = 20 * 4/5 = 16 litres
Water in the 20 litres of mixture = 20 * 1/5 = 4 litres
According to the question,
(4x – 16)/(x – 4 + 6) = 8/3
(4x – 16)/(x + 2) = 8/3
12x – 48 = 8x + 16
4x = 16 + 48
4x = 64
X = 16
Initial quantity of Milk in the vessel A = 4* 16 = 64 litres
Quantity II: In vessel B, 15 litres of mixture is taken out and 3 litres of water is added in the mixture, then the ratio of water and milk in the final mixture is 7:9. Find the initial quantity of milk in the vessel
Milk and water ratio = 60: 40
= 3: 2
Milk in the 15 litres of mixture = 15 * 3/5 = 9 litres
Water in the 15 litres of mixture = 15 * 2/5 = 6 litres
According to the question,
(3x – 9)/(2x – 6 + 3) = 9/7
(3x – 9)/(2x – 3) = 9/7
21x – 63 = 18x – 27
3x = 63 – 27
3x = 36
X = 12
Initial quantity of Milk in the vessel A = 3* 12 = 36 litres
Hence, Quantity I > Quantity II
The solution is- total students in each school as per the percentage given is

6). (d), total number of students who have enrolled for coaching institutes A and C together from school P =
20+70 = 90
Total number of students who have enrolled for the same institutes from school = 16+60 = 76
Ratio = 90:76 = 45:38
7). (b), female = 40%*180 = 72, 20% of female is from school Q = 14
Female from other school = 72-14 = 58
So the difference = 58-14 = 40
8). (b), average number of student = 20+80+54+90/4= 61
9). (e), percentage = 20+16/70+40 ∗ 100 = 32 8/11%
10). (c), percentage = (58-42)/58*100 = 27.58%