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Raja was on a long distance trip. He travelled by air 2/5 of the distance which was 1200 km. Then, he hired a car and travelled 1/3 of the whole trip. Thereafter, he completed the rest of the journey by train. Calculate the distance that Raja travelled by train.
- a)480 km
- b)800 km
- c)1600 km
- d)1800 km
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Raja was on a long distance trip. He travelled by air 2/5 of the dista...
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To find the distance that Raja travelled by train, we need to subtract the distances he travelled by air and by car from the total distance of the trip.
Given:
Distance travelled by air = 2/5 of the total distance = 1200 km
Let's calculate the total distance of the trip:
We know that the distance travelled by air is 2/5 of the total distance, so the remaining distance (3/5) is covered by car and train.
Let the total distance be 'd'.
Therefore, (3/5)d = d - 1200 km
Multiplying both sides of the equation by 5/3, we get:
d = (5/3)(d - 1200 km)
d = (5/3)d - 2000 km
d - (5/3)d = -2000 km
(3/3)d - (5/3)d = -2000 km
(-2/3)d = -2000 km
Multiplying both sides of the equation by -3/2, we get:
d = (-3/2)(-2000 km)
d = 3000 km
So, the total distance of the trip is 3000 km.
Now, let's calculate the distance Raja travelled by car:
Distance travelled by car = 1/3 of the total distance = (1/3)(3000 km) = 1000 km
Finally, we can calculate the distance Raja travelled by train:
Distance travelled by train = Total distance - Distance travelled by air - Distance travelled by car
Distance travelled by train = 3000 km - 1200 km - 1000 km
Distance travelled by train = 800 km
Therefore, Raja travelled a distance of 800 km by train.
Hence, the correct answer is option B) 800 km.
Given:
Distance travelled by air = 2/5 of the total distance = 1200 km
Let's calculate the total distance of the trip:
We know that the distance travelled by air is 2/5 of the total distance, so the remaining distance (3/5) is covered by car and train.
Let the total distance be 'd'.
Therefore, (3/5)d = d - 1200 km
Multiplying both sides of the equation by 5/3, we get:
d = (5/3)(d - 1200 km)
d = (5/3)d - 2000 km
d - (5/3)d = -2000 km
(3/3)d - (5/3)d = -2000 km
(-2/3)d = -2000 km
Multiplying both sides of the equation by -3/2, we get:
d = (-3/2)(-2000 km)
d = 3000 km
So, the total distance of the trip is 3000 km.
Now, let's calculate the distance Raja travelled by car:
Distance travelled by car = 1/3 of the total distance = (1/3)(3000 km) = 1000 km
Finally, we can calculate the distance Raja travelled by train:
Distance travelled by train = Total distance - Distance travelled by air - Distance travelled by car
Distance travelled by train = 3000 km - 1200 km - 1000 km
Distance travelled by train = 800 km
Therefore, Raja travelled a distance of 800 km by train.
Hence, the correct answer is option B) 800 km.
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