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 10 male passengers alighted at Orchard Station and 10 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:_______________




2)  

There were 13 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 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 27 male passengers alighted at Orchard Station and 27 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 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 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 211 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 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 13 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 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 12 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 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 24 male passengers alighted at Orchard Station and 24 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 45 male passengers alighted at Orchard Station and 45 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 10 male passengers alighted at Orchard Station and 10 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: 280 


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 →  4 units→  4 x 7 = 28 units
Difference →  3 units→  3 x 7 =  21 units

  

After

Male passengers→ 2 units→   2 x 3 = 6 units
Female passengers→ 9 units→  9 x 3 = 27 units
Difference→7 units→ 7 x 3 = 21 units

 

Therefore,

Decrease in female passengers: 28 - 27 = 1 units

1 units → 10

1 unit → 10 ÷ 1

              = 10

28 units → 28 x 10

              = 280 female passengers at first



2)  

There were 13 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 211 as many male passengers as female passengers on the train. How many female passengers were there on board the train at first

Answer: 297 


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 → 55

1 unit → 55 ÷ 5

              = 11

27 units → 27 x 11

              = 297 female passengers at first



3)  

There were 29 as many male passengers as female passengers on board a train. After 27 male passengers alighted at Orchard Station and 27 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: 405 


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 → 27

1 unit → 27 ÷ 3

              = 9

45 units → 45 x 9

              = 405 female passengers at first



4)  

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

Answer: 210 


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 → 30

1 unit → 30 ÷ 3

              = 10

21 units → 21 x 10

              = 210 female passengers at first



5)  

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

Answer: 462 


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 → 21

1 unit → 21 ÷ 3

              = 7

66 units → 66 x 7

              = 462 female passengers at first



6)  

There were 13 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 211 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 →  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 → 50

1 unit → 50 ÷ 5

              = 10

27 units → 27 x 10

              = 270 female passengers at first



7)  

There were 12 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 29 as many male passengers as female passengers on the train. How many female passengers were there on board the train at first

Answer: 98 


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 → 35

1 unit → 35 ÷ 5

              = 7

14 units → 14 x 7

              = 98 female passengers at first



8)  

There were 29 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 16 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 →  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 → 24

1 unit → 24 ÷ 3

              = 8

45 units → 45 x 8

              = 360 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 45 male passengers alighted at Orchard Station and 45 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: 486 


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 → 45

1 unit → 45 ÷ 5

              = 9

54 units → 54 x 9

              = 486 female passengers at first