Scroll:Fractions >> Four Operations of Fractions >> ps (3032)

Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.


 

1)  

There were 29 as many male passengers as female passengers on board a train. After 56 male passengers alighted at Orchard Station and 56 female passengers alighted at Sommerset Station, there were 18 as many male passengers as female passengers on the train. How many female passengers were there on board the train at first

 


Answer:_______________




2)  

There were 12 as many male passengers as female passengers on board a train. After 30 male passengers alighted at Orchard Station and 30 female passengers alighted at Sommerset Station, there were 27 as many male passengers as female passengers on the train. How many female passengers were there on board the train at first

 


Answer:_______________




3)  

There were 14 as many male passengers as female passengers on board a train. After 30 male passengers alighted at Orchard Station and 30 female passengers alighted at Sommerset Station, there were 211 as many male passengers as female passengers on the train. How many female passengers were there on board the train at first

 


Answer:_______________




4)  

There were 12 as many male passengers as female passengers on board a train. After 30 male passengers alighted at Orchard Station and 30 female passengers alighted at Sommerset Station, there were 29 as many male passengers as female passengers on the train. How many female passengers were there on board the train at first

 


Answer:_______________




5)  

There were 29 as many male passengers as female passengers on board a train. After 50 male passengers alighted at Orchard Station and 50 female passengers alighted at Sommerset Station, there were 17 as many male passengers as female passengers on the train. How many female passengers were there on board the train at first

 


Answer:_______________




6)  

There were 29 as many male passengers as female passengers on board a train. After 55 male passengers alighted at Orchard Station and 55 female passengers alighted at Sommerset Station, there were 17 as many male passengers as female passengers on the train. How many female passengers were there on board the train at first

 


Answer:_______________




7)  

There were 13 as many male passengers as female passengers on board a train. After 15 male passengers alighted at Orchard Station and 15 female passengers alighted at Sommerset Station, there were 29 as many male passengers as female passengers on the train. How many female passengers were there on board the train at first

 


Answer:_______________




8)  

There were 13 as many male passengers as female passengers on board a train. After 18 male passengers alighted at Orchard Station and 18 female passengers alighted at Sommerset Station, there were 29 as many male passengers as female passengers on the train. How many female passengers were there on board the train at first

 


Answer:_______________




9)  

There were 13 as many male passengers as female passengers on board a train. After 30 male passengers alighted at Orchard Station and 30 female passengers alighted at Sommerset Station, there were 211 as many male passengers as female passengers on the train. How many female passengers were there on board the train at first

 


Answer:_______________




10)  

There were 211 as many male passengers as female passengers on board a train. After 7 male passengers alighted at Orchard Station and 7 female passengers alighted at Sommerset Station, there were 16 as many male passengers as female passengers on the train. How many female passengers were there on board the train at first

 


Answer:_______________




 

1)  

There were 29 as many male passengers as female passengers on board a train. After 56 male passengers alighted at Orchard Station and 56 female passengers alighted at Sommerset Station, there were 18 as many male passengers as female passengers on the train. How many female passengers were there on board the train at first

Answer: 504 


SOLUTION 1 :

Since the number of male and female passengers who alighted from the train is the same, there is a constant difference.

Before 

Male passengers →  2 units→   2 x 7 = 14 units
Female passengers →  9 units→  9 x 7 = 63 units
Difference →  7 units→  7 x 7 =  49 units

  

After

Male passengers→ 1 unit→   1 x 7 = 7 units
Female passengers→ 8 units→  8 x 7 = 56 units
Difference→7 units→ 7 x 7 = 49 units

 

Therefore,

Decrease in female passengers: 63 - 56 = 7 units

7 units → 56

1 unit → 56 ÷ 7

              = 8

63 units → 63 x 8

              = 504 female passengers at first



2)  

There were 12 as many male passengers as female passengers on board a train. After 30 male passengers alighted at Orchard Station and 30 female passengers alighted at Sommerset Station, there were 27 as many male passengers as female passengers on the train. How many female passengers were there on board the train at first

Answer: 100 


SOLUTION 1 :

Since the number of male and female passengers who alighted from the train is the same, there is a constant difference.

Before 

Male passengers →  1 unit→   1 x 5 = 5 units
Female passengers →  2 units→  2 x 5 = 10 units
Difference →  1 units→  1 x 5 =  5 units

  

After

Male passengers→ 2 units→   2 x 1 = 2 units
Female passengers→ 7 units→  7 x 1 = 7 units
Difference→5 units→ 5 x 1 = 5 units

 

Therefore,

Decrease in female passengers: 10 - 7 = 3 units

3 units → 30

1 unit → 30 ÷ 3

              = 10

10 units → 10 x 10

              = 100 female passengers at first



3)  

There were 14 as many male passengers as female passengers on board a train. After 30 male passengers alighted at Orchard Station and 30 female passengers alighted at Sommerset Station, there were 211 as many male passengers as female passengers on the train. How many female passengers were there on board the train at first

Answer: 360 


SOLUTION 1 :

Since the number of male and female passengers who alighted from the train is the same, there is a constant difference.

Before 

Male passengers →  1 unit→   1 x 9 = 9 units
Female passengers →  4 units→  4 x 9 = 36 units
Difference →  3 units→  3 x 9 =  27 units

  

After

Male passengers→ 2 units→   2 x 3 = 6 units
Female passengers→ 11 units→  11 x 3 = 33 units
Difference→9 units→ 9 x 3 = 27 units

 

Therefore,

Decrease in female passengers: 36 - 33 = 3 units

3 units → 30

1 unit → 30 ÷ 3

              = 10

36 units → 36 x 10

              = 360 female passengers at first



4)  

There were 12 as many male passengers as female passengers on board a train. After 30 male passengers alighted at Orchard Station and 30 female passengers alighted at Sommerset Station, there were 29 as many male passengers as female passengers on the train. How many female passengers were there on board the train at first

Answer: 84 


SOLUTION 1 :

Since the number of male and female passengers who alighted from the train is the same, there is a constant difference.

Before 

Male passengers →  1 unit→   1 x 7 = 7 units
Female passengers →  2 units→  2 x 7 = 14 units
Difference →  1 units→  1 x 7 =  7 units

  

After

Male passengers→ 2 units→   2 x 1 = 2 units
Female passengers→ 9 units→  9 x 1 = 9 units
Difference→7 units→ 7 x 1 = 7 units

 

Therefore,

Decrease in female passengers: 14 - 9 = 5 units

5 units → 30

1 unit → 30 ÷ 5

              = 6

14 units → 14 x 6

              = 84 female passengers at first



5)  

There were 29 as many male passengers as female passengers on board a train. After 50 male passengers alighted at Orchard Station and 50 female passengers alighted at Sommerset Station, there were 17 as many male passengers as female passengers on the train. How many female passengers were there on board the train at first

Answer: 540 


SOLUTION 1 :

Since the number of male and female passengers who alighted from the train is the same, there is a constant difference.

Before 

Male passengers →  2 units→   2 x 6 = 12 units
Female passengers →  9 units→  9 x 6 = 54 units
Difference →  7 units→  7 x 6 =  42 units

  

After

Male passengers→ 1 unit→   1 x 7 = 7 units
Female passengers→ 7 units→  7 x 7 = 49 units
Difference→6 units→ 6 x 7 = 42 units

 

Therefore,

Decrease in female passengers: 54 - 49 = 5 units

5 units → 50

1 unit → 50 ÷ 5

              = 10

54 units → 54 x 10

              = 540 female passengers at first



6)  

There were 29 as many male passengers as female passengers on board a train. After 55 male passengers alighted at Orchard Station and 55 female passengers alighted at Sommerset Station, there were 17 as many male passengers as female passengers on the train. How many female passengers were there on board the train at first

Answer: 594 


SOLUTION 1 :

Since the number of male and female passengers who alighted from the train is the same, there is a constant difference.

Before 

Male passengers →  2 units→   2 x 6 = 12 units
Female passengers →  9 units→  9 x 6 = 54 units
Difference →  7 units→  7 x 6 =  42 units

  

After

Male passengers→ 1 unit→   1 x 7 = 7 units
Female passengers→ 7 units→  7 x 7 = 49 units
Difference→6 units→ 6 x 7 = 42 units

 

Therefore,

Decrease in female passengers: 54 - 49 = 5 units

5 units → 55

1 unit → 55 ÷ 5

              = 11

54 units → 54 x 11

              = 594 female passengers at first



7)  

There were 13 as many male passengers as female passengers on board a train. After 15 male passengers alighted at Orchard Station and 15 female passengers alighted at Sommerset Station, there were 29 as many male passengers as female passengers on the train. How many female passengers were there on board the train at first

Answer: 105 


SOLUTION 1 :

Since the number of male and female passengers who alighted from the train is the same, there is a constant difference.

Before 

Male passengers →  1 unit→   1 x 7 = 7 units
Female passengers →  3 units→  3 x 7 = 21 units
Difference →  2 units→  2 x 7 =  14 units

  

After

Male passengers→ 2 units→   2 x 2 = 4 units
Female passengers→ 9 units→  9 x 2 = 18 units
Difference→7 units→ 7 x 2 = 14 units

 

Therefore,

Decrease in female passengers: 21 - 18 = 3 units

3 units → 15

1 unit → 15 ÷ 3

              = 5

21 units → 21 x 5

              = 105 female passengers at first



8)  

There were 13 as many male passengers as female passengers on board a train. After 18 male passengers alighted at Orchard Station and 18 female passengers alighted at Sommerset Station, there were 29 as many male passengers as female passengers on the train. How many female passengers were there on board the train at first

Answer: 126 


SOLUTION 1 :

Since the number of male and female passengers who alighted from the train is the same, there is a constant difference.

Before 

Male passengers →  1 unit→   1 x 7 = 7 units
Female passengers →  3 units→  3 x 7 = 21 units
Difference →  2 units→  2 x 7 =  14 units

  

After

Male passengers→ 2 units→   2 x 2 = 4 units
Female passengers→ 9 units→  9 x 2 = 18 units
Difference→7 units→ 7 x 2 = 14 units

 

Therefore,

Decrease in female passengers: 21 - 18 = 3 units

3 units → 18

1 unit → 18 ÷ 3

              = 6

21 units → 21 x 6

              = 126 female passengers at first



9)  

There were 13 as many male passengers as female passengers on board a train. After 30 male passengers alighted at Orchard Station and 30 female passengers alighted at Sommerset Station, there were 211 as many male passengers as female passengers on the train. How many female passengers were there on board the train at first

Answer: 162 


SOLUTION 1 :

Since the number of male and female passengers who alighted from the train is the same, there is a constant difference.

Before 

Male passengers →  1 unit→   1 x 9 = 9 units
Female passengers →  3 units→  3 x 9 = 27 units
Difference →  2 units→  2 x 9 =  18 units

  

After

Male passengers→ 2 units→   2 x 2 = 4 units
Female passengers→ 11 units→  11 x 2 = 22 units
Difference→9 units→ 9 x 2 = 18 units

 

Therefore,

Decrease in female passengers: 27 - 22 = 5 units

5 units → 30

1 unit → 30 ÷ 5

              = 6

27 units → 27 x 6

              = 162 female passengers at first



10)  

There were 211 as many male passengers as female passengers on board a train. After 7 male passengers alighted at Orchard Station and 7 female passengers alighted at Sommerset Station, there were 16 as many male passengers as female passengers on the train. How many female passengers were there on board the train at first

Answer: 385 


SOLUTION 1 :

Since the number of male and female passengers who alighted from the train is the same, there is a constant difference.

Before 

Male passengers →  2 units→   2 x 5 = 10 units
Female passengers →  11 units→  11 x 5 = 55 units
Difference →  9 units→  9 x 5 =  45 units

  

After

Male passengers→ 1 unit→   1 x 9 = 9 units
Female passengers→ 6 units→  6 x 9 = 54 units
Difference→5 units→ 5 x 9 = 45 units

 

Therefore,

Decrease in female passengers: 55 - 54 = 1 units

1 units → 7

1 unit → 7 ÷ 1

              = 7

55 units → 55 x 7

              = 385 female passengers at first