Speed, Time and Distance
 A train starts from A at 7 a.m. towards B with speed 50 km/h. Another train starts from B at 8 a.m. with speed 60 km/h towards A. Both of them meet at 10 a.m. at C. The ratio of the distance AC to BC is

 5 : 6
 5 : 4
 6 : 5
 4 : 5

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AC = Distance covered by train starting from A in 3 hours
= 50 × 3 = 150 km
BC = Distance covered by train starting from B in 2 hours
= 60 ×2 = 120 km
∴ AC : BC = 150 : 120 = 5 : 4Correct Option: B
AC = Distance covered by train starting from A in 3 hours
= 50 × 3 = 150 km
BC = Distance covered by train starting from B in 2 hours
= 60 ×2 = 120 km
∴ AC : BC = 150 : 120 = 5 : 4
 The ratio of length of two trains is 5 : 3 and the ratio of their speed is 6 : 5. The ratio of time
taken by them to cross a pole is

 5 : 6
 11 : 8
 25 : 18
 27 : 16

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Required ratio
= 5 : 3 = 30 × 5 : 30 × 3 6 5 6 5
= 25 : 18Correct Option: C
Required ratio
= 5 : 3 = 30 × 5 : 30 × 3 6 5 6 5
= 25 : 18
 The speed of A and B are in the ratio 3 : 4. A takes 20 minutes more than B to reach a destination. In what time does A reach the destination ?


1 1 hours 3  2 hours

2 2 hours 3 
1 2 hours 3


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Ratio of speed = 3 : 4
Ratio of time taken = 4 : 3
Let the time taken by A and B be 4x hours and 3 x hours respectively.Then, 4x–3x = 20 ⇒ x = 1 60 3
∴ Time taken by A = 4x hours= 4 × 1 hours 3 = 1 1 hours 3
Second Method :
Here, S_{1} = 3x, S_{2} = 4xt_{2}= y, t_{1} = y + 20 = y + 1 60 3
S_{1}t_{1} = S_{2}t_{2}3x y + 1 = 4xy 3 ∴ Time taken by A = 1 + 1 = 1 1 hours 3 3 Correct Option: A
Ratio of speed = 3 : 4
Ratio of time taken = 4 : 3
Let the time taken by A and B be 4x hours and 3 x hours respectively.Then, 4x–3x = 20 ⇒ x = 1 60 3
∴ Time taken by A = 4x hours= 4 × 1 hours 3 = 1 1 hours 3
Second Method :
Here, S_{1} = 3x, S_{2} = 4xt_{2}= y, t_{1} = y + 20 = y + 1 60 3
S_{1}t_{1} = S_{2}t_{2}3x y + 1 = 4xy 3 ∴ Time taken by A = 1 + 1 = 1 1 hours 3 3
 In covering a certain distance, the speed of A and B are in the ratio of 3 : 4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is :

 1 hour

1 1 hours 2  2 hours

2 1 hours 2

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Let the distance of destination be D km
Let the speed of A = 3x km/hr
then speed of B = 4x km/hr
∴ According to question,D − D = 30 minutes 3x 4x = 1 hr 2 ∴ D = 1 12x 2 ⇒ D = 4 = 2 hours 3x 2
Hence, time taken by A to reach
destination = 2hrs.
Second Method :
Here, S_{1} = 3x, S_{2} = 4xt_{2}= y, t_{1} = y + 30 = y + 1 60 2
S_{1}t_{1} = S_{2}t_{2}3x × y + 1 = 4 x × y 2 3y + 3 = 4y 2 y = 3 2 ∴ Time taken by A = 3 + 1 = 2 hrs. 2 2 Correct Option: C
Let the distance of destination be D km
Let the speed of A = 3x km/hr
then speed of B = 4x km/hr
∴ According to question,D − D = 30 minutes 3x 4x = 1 hr 2 ∴ D = 1 12x 2 ⇒ D = 4 = 2 hours 3x 2
Hence, time taken by A to reach
destination = 2hrs.
Second Method :
Here, S_{1} = 3x, S_{2} = 4xt_{2}= y, t_{1} = y + 30 = y + 1 60 2
S_{1}t_{1} = S_{2}t_{2}3x × y + 1 = 4 x × y 2 3y + 3 = 4y 2 y = 3 2 ∴ Time taken by A = 3 + 1 = 2 hrs. 2 2
 In covering a certain distance, the speed of A and B are in the ratio of 3 : 4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is :

 1 hour

1 1 hours 2  2 hours

2 1 hours 2

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Let the distance of destination be D km
Let the speed of A = 3x km/hr
then speed of B = 4x km/hr
∴ According to question,D − D = 30 minutes 3x 4x = 1 hr 2 ∴ D = 1 12x 2 ⇒ D = 4 = 2 hours 3x 2
Hence, time taken by A to reach
destination = 2hrs.
Second Method :
Here, S_{1} = 3x, S_{2} = 4xt_{2}= y, t_{1} = y + 30 = y + 1 60 2
S_{1}t_{1} = S_{2}t_{2}3x × y + 1 = 4 x × y 2 3y + 3 = 4y 2 y = 3 2 ∴ Time taken by A = 3 + 1 = 2 hrs. 2 2 Correct Option: C
Let the distance of destination be D km
Let the speed of A = 3x km/hr
then speed of B = 4x km/hr
∴ According to question,D − D = 30 minutes 3x 4x = 1 hr 2 ∴ D = 1 12x 2 ⇒ D = 4 = 2 hours 3x 2
Hence, time taken by A to reach
destination = 2hrs.
Second Method :
Here, S_{1} = 3x, S_{2} = 4xt_{2}= y, t_{1} = y + 30 = y + 1 60 2
S_{1}t_{1} = S_{2}t_{2}3x × y + 1 = 4 x × y 2 3y + 3 = 4y 2 y = 3 2 ∴ Time taken by A = 3 + 1 = 2 hrs. 2 2