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 14 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 211 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 77 male passengers alighted at Orchard Station and 77 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:_______________




3)  

There were 29 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 16 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 29 as many male passengers as female passengers on board a train. After 40 male passengers alighted at Orchard Station and 40 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 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:_______________




7)  

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:_______________




8)  

There were 29 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 16 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 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:_______________




10)  

There were 29 as many male passengers as female passengers on board a train. After 35 male passengers alighted at Orchard Station and 35 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:_______________




 

1)  

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

Answer: 216 


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 → 18

1 unit → 18 ÷ 3

              = 6

36 units → 36 x 6

              = 216 female passengers at first



2)  

There were 12 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 211 as many male passengers as female passengers on the train. How many female passengers were there on board the train at first

Answer: 198 


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 →  2 units→  2 x 9 = 18 units
Difference →  1 units→  1 x 9 =  9 units

  

After

Male passengers→ 2 units→   2 x 1 = 2 units
Female passengers→ 11 units→  11 x 1 = 11 units
Difference→9 units→ 9 x 1 = 9 units

 

Therefore,

Decrease in female passengers: 18 - 11 = 7 units

7 units → 77

1 unit → 77 ÷ 7

              = 11

18 units → 18 x 11

              = 198 female passengers at first



3)  

There were 29 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 16 as many male passengers as female passengers on the train. How many female passengers were there on board the train at first

Answer: 315 


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 → 21

1 unit → 21 ÷ 3

              = 7

45 units → 45 x 7

              = 315 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 29 as many male passengers as female passengers on board a train. After 40 male passengers alighted at Orchard Station and 40 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: 432 


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 → 40

1 unit → 40 ÷ 5

              = 8

54 units → 54 x 8

              = 432 female passengers at first



6)  

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



7)  

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



8)  

There were 29 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 16 as many male passengers as female passengers on the train. How many female passengers were there on board the train at first

Answer: 270 


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 → 18

1 unit → 18 ÷ 3

              = 6

45 units → 45 x 6

              = 270 female passengers at first



9)  

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



10)  

There were 29 as many male passengers as female passengers on board a train. After 35 male passengers alighted at Orchard Station and 35 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: 378 


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 → 35

1 unit → 35 ÷ 5

              = 7

54 units → 54 x 7

              = 378 female passengers at first