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Quantity I and II
Directions (1-5): Each question below contains a statement followed by Quantity I and Quantity II. Find the relationship among them and mark your answer accordingly. Give answer as,
a)Quantity I > Quantity II
b) Quantity I ≥ Quantity II
c)Quantity II > Quantity I
d)Quantity II ≥ Quantity I
e)Quantity I = Quantity II or Relation cannot be established
1) Quantity I: The ratio of present age of Nive and Renuka is 4: 7. Nive is 8 years younger than Bhairavi. After 7 years, Bhairavi’s age is 35. Then find the present age of Renuka?
Quantity II:Â The sum of the present age Rahul and his son is 40 years. 15 years after, the ratio of Rahul and his son is 5: 2. Then find the present age of Rahul?
2) Quantity I:Â A boat can cover 80 km downstream in 48 minutes. If the speed of the current is 3/7 of the boat in still water, then how much distance (in km) can the boat cover upstream in 300 minutes?
Quantity II:Â Speed of a man in still water is 12 km/hr and the river is running at 6 km/hr. The total time taken to go to a place and come back is 40 hours. Find the distance travelled by the man?
3) Quantity I:Â A necklace was sold for Rs. 5500 with a profit of 10 %. If it were sold for Rs. 5900, then what would have been the percentage of profit?
Quantity II:Â A person bought two showcases for Rs. 5000 each. He sold one at a profit of 10 % and the other at a loss of 5 %. What would be his overall profit or loss percentage in the whole transaction?
4) Quantity I:Â A bucket contains some quantity of milk and water in the ratio of 3: 2. If 15 litres of mixture is drawn out and replaced with water and the ratio of milk and water becomes 21: 29, then find the initial quantity of mixture?
Quantity II:Â How many litres of water should be added to a 150 litres mixture containing milk and water in the ratio of 2: 1 such that the resultant mixture has 40 % milk in it?
5) Quantity I:Â The difference between the simple interest and compound interest on a certain sum of money for 2 years at 10 % per annum is Rs. 600. Find the sum?
Quantity II:Â A certain sum of money invested for a period of 5 years at 8 % per annum, simple interest earned is Rs. 30000. Find the principle?
Application Sums
6) A box contains 8 Pink balls, 5 black balls, 4 orange balls and 3 white balls. If four balls are drawn out randomly, then the probability of getting a different colour balls?
A) 11/35
B) 32/323
C) 18/189
D) 34/77
E) None of these
7) The ratio of the age of P after 3 years and 6 years ago, the age of Q is 3: 4. The present age of R is 2 times the present age of P. The difference between the present age of Q and R is 6 years. Find the present age of P?
A) 22 years
B) 20 years
C) 24 years
D) 16 years
E) None of these
8) The volume of cylinder 1 and 2 is in the ratio of 3: 1 and the height of the cylinder 1 and 2 is in the ratio of 3: 4. Find the ratio between the radius of cylinder 1 and cylinder 2?
A) 7: 5
B) 5: 2
C) 4: 3
D) 2: 1
E) None of these
9) The present age of Janvi and her husband is 5: 6. The present age Janvi’s daughter is (1/5) of Janvi’s present age. Janvi’s daughter is 3 years younger than her son. Find the sum of the present age of Janvi and her husband, if the age of Janvi’s son, after 7 years is 15 years?
A) 58 years
B) 66 years
C) 55 years
D) 62 years
E) None of these
10) The length of train A is 200 m and that of train B is 300 m. These two trains are running in the opposite direction with the velocities of 60 km/hr and 40 km/hr respectively. Find the time taken to cross each other?
A) 14 sec
B) 21 sec
C) 18 sec
D) 25 sec
E) None of these
Answers :
Directions (1-5) :
1) Answer: E
Quantity I:
The ratio of present age of Nive and Renuka = 4: 7
Nive = Bhairavi – 8
After 7 years, Bhairavi’s age = 35
Present age of Bhairavi = 28
Nive = 28 – 8 = 20
4’s = 20
1’s = 5
Present age of Renuka = 7’s = 35 years
Quantity II:
The sum of the present age Rahul and his son = 40 years
Rahul + Rahul’s son = 40
15 years after, the ratio of the age of Rahul and his son = 5: 2
According to the question,
5x – 15 + 2x – 15 = 40
7x = 40 + 30
7x = 70
x = 10
Present age of Rahul= 5x – 15 = 35 years
Quantity I = Quantity II
2) Answer: A
Quantity I:
Speed of downstream = (80 * 60)/48 = 100 km/hr
Speed of current: Speed of still water = 3: 7
Speed of upstream = Speed of boat in still water – speed of Current
100 = 10x
= > x = 10
Speed of current = 30 km/hr
Speed of boat in still water = 70 km/hr
Speed of upstream= Speed of boat in still water – speed of Current
= > 70 – 30 = 40 km/hr
Speed = 40 km/hr, Time = 300 minutes
Distance = 40 * (300/60)Â =Â 200 km
Quantity II:
Speed of downstream = 12 + 6 = 18 km/hr
Speed of upstream = 12 – 6 = 6 km/hr
Let the distance travelled be x,
(x/18) + (x/6) = 40
x = 180 km
(Or)
Distance = Time *[(Speed of Still water2 – speed of Stream2)/(2*Speed of Still water)]
= > Distance = 40 * [(122 – 62)/(2 * 12)]
= > Distance = 40 * [(144 – 36)/24]
= > Distance = 180 km
Quantity I > Quantity II
3) Answer: A
Quantity I:
According to the question,
(110/100) * CP = 5500
CP = 5500 * (10/11) = Rs. 5000
SP = 5900
Profit % = (Profit/CP) * 100
= > (900/5000) * 100
= > 18 %
Quantity II:
According to the question,
CP1= 5000, Profit = 10 %
SP1 = 5000 * (110/100) = 5500
CP2 = 5000, Loss = 5 %
SP2 = 5000 × (95/100) = 4750
Total selling price = S.P1 + S.P2 = 5500 + 4750 = 10250
Total cost price = 5000 + 5000 = 10000
Profit % = (250/10000) * 100 = 2.5 %
Quantity I > Quantity II
4) Answer: C
Quantity I:
Total quantity of mixture = 15 litres
Water = 15 * (2/5) = 6 lit, Milk = 15 * (3/5) = 9 lit
Given,
= > (3x – 9)/(2x – 6 + 15) = 21/29
= > 87x – 261 = 42x + 189
= > 45x = 450
= > x = 10
Initial quantity of milk = 5x = 50 litres
Quantity II:
Total mixture = 150 litres
Milk = 100 lit, water = 50 lit
According to the question,
100/(50 + x) = 40/60
150 = 50 + x
x = 100 litres
Quantity I < Quantity II
5) Answer: C
Quantity I:
The difference between the simple interest and compound interest for 2 years,
Diff = Sum * (r/100)2
600 = Sum * (10/100)2
(600 * 100 * 100)/100 = Sum
Sum = Rs. 60000
Quantity II:
I = Pnr/100
30000 = (P * 5 * 8)/100
(30000 * 100)/40 = P
Principle = Rs. 75000
Quantity II > Quantity I
Directions (6-10) :
6) Answer: B
Total probability n(S) = 20C4
Required probability = n(E) = 8C1Â and 5C1Â and 4C1Â and 3C1
P(E) = n(E)/n(S)
P(E) = (8C1Â and 5C1Â and 4C1Â and 3C1)/20C4
P(E) = 32/323
7) Answer: C
The ratio of 3 years after, the age of P and 6 years ago, the age of Q = 3: 4 (3x, 4x)
Present age of P and Q = 3x – 3, 4x + 6
The age of R = 2 * P = 2 * (3x – 3) = 6x – 6
(6x – 6) – (4x + 6) = 6
6x – 6 – 4x – 6 = 6
2x = 6 + 12
2x = 18
x = 9
Present age of P = 3x – 3 = 27 – 3 = 24 years
8) Answer: D
Volume of the cylinder = πr2h
The ratio of volume of cylinder 1 and 2 = 3: 1
The ratio of height of cylinder 1 and 2 = 3: 4
The ratio between the heights of cylinder 1 to that of cylinder 2,
= > [Ï€ * (3x) * r12]/[Ï€ * (4x) * r22] = (3/1)
= > r12/r22Â = (4/1)
= > r1: r2Â = 2: 1
9) Answer: C
The present age of Janvi and her husband = 5: 6 (5x, 6x)
The present age Janvi’s daughter = (1/5) * Janvi’s present age
Janvi’s daughter = Janvi’s son – 3
Janvi’s son after 7 years = 15 years
Janvi’s son’s present age = 8 years
Janvi’s daughter = 8 – 3 = 5 years
Janvi’s present age = 5 * 5 = 25 years
5’s = 25
1’s = 5
Present age of Janvi’s husband = 6x = 30 years
Required sum = 25 + 30 = 55 years
10) Answer: C
T = D/S
T = (200 + 300)/[(60 + 40) * (5/18)]
T = (500 * 18)/(100 * 5)
T = 18 sec
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