Directions: In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis. (only quantity is to be considered)
1
Quantity I : A train can cross a pole and platform having a length of 330 m in 8 seconds and 23 seconds respectively. Find the speed of the train in km/hr.
 
Quantity II : When the average speed of the car is decreased by 5 km/hr, it reaches its destination 9 minutes late. Find the original average speed(in km/hr) of the car if the destination is 180 km from the starting point.
» Explain it
C
Quantity I:

Let the length of the train be ‘x’ m

So, the speed of the train =  x
8

Also, the speed of train =  x + 330
23

So,  x  =  x + 330
8 23

23x = 8x + 2640

15x = 2640; x = 176

So, the speed of the train =  176  = 22 m/s = 79.2 km/h
8

Quantity II:

Let the original average speed of the car be ‘x’ km/h

According to the question,

180  –  180  =  9
x – 5 x 60

x2 – 5x – 6000 = 0

x2 – 80x + 75x – 6000 = 0

x (x – 80) + 75(x – 80) = 0

(x – 80)(x + 75) = 0

x = 80, – 75

Speed can’t be negative. So, the value of ‘x’ = 80

So, the original average speed of the car = 80 km/hr

So, Quantity I < Quantity II

So option (C) is the correct answer.
2
Quantity I : Pipes A and B individually can fill the empty tank in 20 hours and 25 hours respectively. Pipe C alone can empty the full tank in 40 hours. Pipe A is opened at the start and after 5 hours pipe B is also opened. After 4 more hours pipe C is also opened. In how many hours the tank is filled completely?
 
Quantity II : A and B together can do a piece of work in 6 hours. A is 50% more efficient than B. In how many hours, A alone can complete the work?
» Explain it
A
Quantity I:

Let the capacity of the tank = 200 litres (LCM of 20, 25 and 40)

Quantity of water filled by pipe A alone in one hour

200  = 10 litres
20

Quantity of water filled by pipe B alone in one hour

200  = 8 litres
25

Quantity of water emptied by pipe C alone in one hour

200  = 5 litres
40

Quantity of water filled by pipe A alone in five hours = 10 × 5 = 50 litres

Quantity of water filled by pipe A and B together in 4 hour = (10 + 8) × 4 = 72 litres

Quantity of remaining water to be filled by pipes A, B and C together = 200 – 50 – 72 = 78 litres

Time taken by pipes A, B and C together to fill the remaining 78 litres

78  =  78  = 6 hours
10 + 8 – 5 13

So, total time taken to fill the empty tank = (5 + 4 + 6) = 15 hours

Quantity II:

Let the time taken by B alone to complete the work be ‘x’ hours

So, the time taken by A alone to complete the work

x  =  2x  hours
1.5 3

So, according to question,

1  +  3  x =  1
x 2 6

5x  =  1  ; x = 15
2 6

So, time taken by A alone to complete the work

15  = 10 hours
1.5

So, Quantity I > Quantity II

So option (A) is the correct answer.
» Explain it
A
Quantity I:
 
2131141  =  (21316 71 ×  213 15
 
Number Divisor Remainder
21316 17 1
2131 17 9
2132 17 -4
2134 17 -1
2138 17 1
21315 17 2
 
Therefore, required remainder = (1)71 × 2 = 2
 

Quantity II:
 
Unit digit of (any odd number except 5 at unit’s place)4n =1



Therefore, unit digit of  

So, Quantity I > Quantity II

So option A is the correct answer. 
4
Quantity I : Mr. Shukla spent 24% of his monthly income on EMI of house and Car, 12% of his children’s education, 20% and 5% of the remaining monthly income on Investment and Entertainment, respectively. If he saves Rs. 21600, then find the amount spent by Mr. Shukla on Entertainment. 
 
Quantity II : The ratio of the monthly income of Raju and Vinesh is 4 : 3 respectively, and the respective ratio of their expenditure is 5 : 4. Raju and Vinesh save Rs. 10000 and Rs. 6000 respectively. If Vinesh gives 5% of his income to his sister, then find the amount given by Vinesh to his sister.
» Explain it
C
Quantity I:

Let the monthly income of Shukla be Rs. ‘100x’

So, amount spends by Shukla on EMI = 0.24×100x=Rs.24x

So, amount spends by Shukla on children’s education = 0.12×100x=Rs.12x

So, remaining income = (100x – 24x – 12x) = Rs.64x

So, the amount spends by Shukla on Investment and Entertainment = (0.20 + 0.05) × 64x = Rs.16x

Therefore, savings = (64x – 16x) = 48x

According to question,

48x = 21600 ; x = 45

So, income of Shukla = 100x = 45000

Therefore, the amount spends by Shukla on Entertainment = 0.05 × 64 × 450 = Rs.1440
 
Quantity II: 
 
Let, the income of Raju and Vinesh be Rs. ‘4x’ and Rs.‘3x’ respectively

According to the question,

(4x – 10000)/(3x – 6000) = 5/4

16x – 40000 = 15x – 30000

x = 10000

So, the income of Vinesh = 3 × 10000 = 30000

Therefore, the amount is given to sister by Vinesh = 0.05 × 30000 = Rs.1500
 
So, Quantity I < Quantity II
 
So option (C) is the correct answer.
5
Quantity I : Sanju can beat Sanjay and Shailesh by 80 meter and 110 meter in a race of 560 m and 440 m respectively, find by what distance Sanjay will beat Shailesh in a race of 480 m?
 
Quantity II : The sum of areas of a rectangular park and square garden is 4300 m2. If the length and breadth of the rectangle is 50% more and 12.5% more than the side of square garden respectively then find the length of rectangular park.
» Explain it
E
Quantity I:

Let, speed of Sanju, Sanjay and Shailesh be ‘A’ m/s, ‘B’ m/s, ‘C’ m/s respectively.

According to question,

560  =  560 – 80
A B

560  =  480
A B

A  =  7
B 6

Also,

440  =  440 – 110
A C

440  =  330
A C

C  =  3
A 4

Using both the equations, we get

A : B : C = 28 : 24 : 21

Ratio of the speed of Sanju: Sanjay: Shailesh = 28 : 24 : 21

Distance run by Sanjay = 480 m

Distance run by Shailesh =  480  × 21 = 420 m
24

So, Sanjay will beat Shailesh by (480 – 420) = 60m

Quantity II:

Let, side of square garden be ‘x’ m

So, length of rectangular garden = 1.5x m

So, breadth of rectangular garden = 1.125m

According to the question,

x2 + 1.5x × 1.125x = 4300

x2 + 1.6875x2 = 4300

2.6875x2 = 4300

x2 4300
2.6875

x2 = 1600

x = 40 m

Therefore, length of rectangular park = 1.5 × 40 = 60m

So, Quantity I = Quantity II or No relation

So, option (E) is the correct answer.