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 15 male passengers alighted at Orchard Station and 15 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:_______________




2)  

There were 13 as many male passengers as female passengers on board a train. After 21 male passengers alighted at Orchard Station and 21 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:_______________




3)  

There were 29 as many male passengers as female passengers on board a train. After 77 male passengers alighted at Orchard Station and 77 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:_______________




4)  

There were 12 as many male passengers as female passengers on board a train. After 25 male passengers alighted at Orchard Station and 25 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 13 as many male passengers as female passengers on board a train. After 24 male passengers alighted at Orchard Station and 24 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:_______________




6)  

There were 211 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 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 45 male passengers alighted at Orchard Station and 45 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:_______________




8)  

There were 29 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 17 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 12 as many male passengers as female passengers on board a train. After 45 male passengers alighted at Orchard Station and 45 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:_______________




10)  

There were 14 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 211 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 15 male passengers alighted at Orchard Station and 15 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: 225 


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 →  9 units→  9 x 5 = 45 units
Difference →  7 units→  7 x 5 =  35 units

  

After

Male passengers→ 1 unit→   1 x 7 = 7 units
Female passengers→ 6 units→  6 x 7 = 42 units
Difference→5 units→ 5 x 7 = 35 units

 

Therefore,

Decrease in female passengers: 45 - 42 = 3 units

3 units → 15

1 unit → 15 ÷ 3

              = 5

45 units → 45 x 5

              = 225 female passengers at first



2)  

There were 13 as many male passengers as female passengers on board a train. After 21 male passengers alighted at Orchard Station and 21 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: 147 


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 → 21

1 unit → 21 ÷ 3

              = 7

21 units → 21 x 7

              = 147 female passengers at first



3)  

There were 29 as many male passengers as female passengers on board a train. After 77 male passengers alighted at Orchard Station and 77 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: 693 


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 → 77

1 unit → 77 ÷ 7

              = 11

63 units → 63 x 11

              = 693 female passengers at first



4)  

There were 12 as many male passengers as female passengers on board a train. After 25 male passengers alighted at Orchard Station and 25 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: 70 


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 → 25

1 unit → 25 ÷ 5

              = 5

14 units → 14 x 5

              = 70 female passengers at first



5)  

There were 13 as many male passengers as female passengers on board a train. After 24 male passengers alighted at Orchard Station and 24 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: 168 


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 → 24

1 unit → 24 ÷ 3

              = 8

21 units → 21 x 8

              = 168 female passengers at first



6)  

There were 211 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 17 as many male passengers as female passengers on the train. How many female passengers were there on board the train at first

Answer: 396 


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 →  11 units→  11 x 6 = 66 units
Difference →  9 units→  9 x 6 =  54 units

  

After

Male passengers→ 1 unit→   1 x 9 = 9 units
Female passengers→ 7 units→  7 x 9 = 63 units
Difference→6 units→ 6 x 9 = 54 units

 

Therefore,

Decrease in female passengers: 66 - 63 = 3 units

3 units → 18

1 unit → 18 ÷ 3

              = 6

66 units → 66 x 6

              = 396 female passengers at first



7)  

There were 13 as many male passengers as female passengers on board a train. After 45 male passengers alighted at Orchard Station and 45 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: 243 


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 → 45

1 unit → 45 ÷ 5

              = 9

27 units → 27 x 9

              = 243 female passengers at first



8)  

There were 29 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 17 as many male passengers as female passengers on the train. How many female passengers were there on board the train at first

Answer: 324 


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 → 30

1 unit → 30 ÷ 5

              = 6

54 units → 54 x 6

              = 324 female passengers at first



9)  

There were 12 as many male passengers as female passengers on board a train. After 45 male passengers alighted at Orchard Station and 45 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 →  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 → 45

1 unit → 45 ÷ 5

              = 9

14 units → 14 x 9

              = 126 female passengers at first



10)  

There were 14 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 211 as many male passengers as female passengers on the train. How many female passengers were there on board the train at first

Answer: 180 


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 → 15

1 unit → 15 ÷ 3

              = 5

36 units → 36 x 5

              = 180 female passengers at first