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Shortcut Trick

Let Length of Train B = L, then Length of Train A = L/2.

Let Speed of Train A = 2x and Speed of Train B = 3x.

Using Distance = Speed × Time: (L/2 + 100) / 5 = 2x and (L + 100) / 6 = 3x.

Ratio of speeds: [(L + 200)/10] / [(L + 100)/6] = 2/3 ⇒ 3(L + 200)/10 = 2(L + 100)/6.

Solving for L: 9L + 1800 = 10L + 1000 ⇒ L = 800 m.

∴ The correct answer is 800 m.

Alternate Method

Given: Ratio of lengths A:B = 1:2. Ratio of speeds A:B = 2:3. Platform = 100 m.

Formula Used: Speed = (Length of Train + Length of Platform) ÷ Time

⇒ Speed of A = (L_A + 100) ÷ 5

⇒ Speed of B = (L_B + 100) ÷ 6

⇒ Let L_B = 2y, then L_A = y

⇒ [(y + 100) ÷ 5] / [(2y + 100) ÷ 6] = 2 ÷ 3

⇒ [6(y + 100)] / [5(2y + 100)] = 2 / 3

⇒ 18(y + 100) = 10(2y + 100)

⇒ 18y + 1800 = 20y + 1000

⇒ 2y = 800

⇒ L_B = 2y = 800 m

∴ The correct answer is 800 m.

Additional Information

Train Crossing Object with Length

When a train crosses a platform, bridge, or another train, the total distance covered is the sum of the train's length and the object's length.

Relative Speed

If two trains are moving in the same direction, relative speed = S₁ − S₂. In opposite directions, relative speed = S₁ + S₂.

Conversion Units

To convert km/hr to m/s, multiply by 5/18. To convert m/s to km/hr, multiply by 18/5.

I. x² + 13x + 42 = 0 

⇒ x² + 7x + 6x + 42 = 0 

⇒ (x + 6)(x + 7) = 0

⇒ x = -6, -7

II. y² – 2y - 63 = 0 

⇒ y² – 9y + 7y - 63 = 0 

⇒ (y – 9)(y + 7) = 0

⇒ y = 9, -7

 

∴ x = y or the relationship between x and y cannot be established.

Given: 

I. x2 - 2x - 8 = 0

II. y2  - 7y - 60 = 0

Concept used:

Using quadratic equation.

Calculation:

From I,

x2 - 2x - 8 = 0

⇒ x² - 4x + 2x - 8 = 0

⇒ x(x - 4) + 2(x - 4) = 0

⇒ (x - 4) (x + 2) = 0

⇒ x = 4, - 2

From II,

y2  - 7y - 60 = 0

⇒ y² - 12y + 5y - 60 = 0

⇒ y(y - 12) + 5(y - 12) = 0

⇒ (y - 12) (y + 5) = 0

⇒ y = 12, -5

Comparison between x and y (via Tabulation):

 

∴ The relationship between x and y cannot be established.

Given:

I) 9x2 - 3x - 2 = 0

II) y2 - 8y + 16 = 0

Concept used:

Using quadratic equation

Calculation:

From I,

9x2 - 3x - 2 = 0

⇒ 9x²  - 6x + 3x - 2 = 0

⇒ 3x(3x - 2) + 1(3x - 2) = 0

⇒ (3x - 2) (3x + 1) = 0

⇒ x = 2/3, - 1/3

From II,

y2 - 8y + 16 = 0

⇒ y² - 4y - 4y + 16 = 0

⇒ y(y - 4) - 4(y - 4) = 0

⇒ (y - 4) (y - 4) = 0

⇒ y = 4, 4

Comparison between x and y (via Tabulation):

 

∴ x < y.

Calculation:

I. x² – 12x + 32 = 0

⇒ x² – 8x – 4x + 32 = 0

⇒ x(x – 8) – 4(x – 8) = 0

⇒ (x – 4)(x – 8) = 0

⇒ x = 4, 8

II.  2y² – 9y + 10 = 0

⇒ 2y² – 4y – 5y + 10 = 0

⇒ 2y(y – 2) – 5(y – 2) = 0

⇒ (2y – 5)(y – 2) = 0

⇒ y = 5/2, 2

 

∴ The relation between x and y is x > y

Calculation∶

I. x² - 15x + 54 = 0

⇒ x² - 6x - 9x + 54 = 0

⇒ x(x - 6) - 9(x - 6) = 0

⇒ (x - 6)(x - 9) = 0

⇒ x = 6, 9

II. y² - 11y + 24 = 0

⇒ y² - 3y - 8y + 24 = 0

⇒ y(y - 3) - 8(y - 3) = 0

⇒ (y - 3)(y - 8) = 0

⇒ y = 3, 8

 

∴ Relationship between x and y cannot be established

Calculation:

Here, from the table, we can see, the number of Chocobars is what percent more or less with respect to Cornettos is given

So, we can say, Arun has 20% more Chocobars than Cornettos 

Let, the total number of Cornettos be 100

So, the ratio of Chocobars and Cornettos = (100 + 20) ∶ 100

⇒ 6 ∶ 5

Similarly, we can say the same for others,

So, put those data in a table, we get,

 

The number of Chocober ice creams Sonal had = 160

The number of Cornetto ice creams she had = 100

So, the required percentage = {(160/100) × 100} = 160%

∴ The number of Chocobar ice creams that Sonal had been 160% of the number of Cornetto ice creams she had.

Alternate Method

Concept used:

Here, we can use the ratio of two ice creams and get the desired result

Calculation:

So, the required percentage = (8/5) × 100 = 160%

∴ The number of Chocobar ice creams that Sonal had been 160% of the number of Cornetto ice creams she had.

Calculation:

Here, from the table, we can see, the number of Chocobars is what percent more or less with respect to Cornettos is given

So, we can say, Arun has 20% more Chocobars than Cornettos 

Let, the total number of Cornettos be 100

So, the ratio of Chocobars and Cornettos = (100 + 20) ∶ 100

⇒ 6 ∶ 5

Similarly, we can say the same for others,

So, put those data on a table, we get,

 

The total number of Cornettos Arun and Kiran has = (100 + 200) = 300

T he total number of Chocobars Barun and Rumi has = (140 + 100) = 240

So, the difference = (300 - 240) = 60

∴ The required difference is 60.

Calculation:

Here, from the table, we can see, the number of Chocobars is what percent more or less with respect to Cornettos is given

So, we can say, Arun has 20% more Chocobars than Cornettos 

Let, the total number of Cornettos be 100

So, the ratio of Chocobars and Cornettos = (100 + 20) ∶ 100

⇒ 6 ∶ 5

Similarly, we can say the same for others,

So, put those data in a table, we get,

 

As per the table, we get

The total number of Chocobar ice creams = (120 + 140 + 180 + 100 + 160) = 700

So, the average number of Chocobar ice creams they have = (700/5) = 140

∴ The average number of Chocobar ice creams they all have is 140.

Calculation:

Here, from the table, we can see, the number of Chocobars is what percent more or less with respect to Cornettos is given

So, we can say, Arun has 20% more Chocobars than Cornettos 

Let, the total number of Cornettos be 100

So, the ratio of Chocobars and Cornettos = (100 + 20) ∶ 100

⇒ 6 ∶ 5

Similarly, we can say the same for others,

So, put those data in a table, we get,

 

The total number of Chocobar ice creams Arun, Kiran and Rumi has = (120 + 180 + 100) = 400

The total number of Cornetto ice creams Barun and Sonal has = (200 + 100) = 300 

So, the ratio will be = 400 ∶ 300 = 4 ∶ 3

∴ The required ratio is 4 ∶ 3.