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CTET & State TET Exam  >  CTET & State TET Questions  >  A person travelled a distance of 50 km in 8 h... Start Learning for Free
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A person travelled a distance of 50 km in 8 hours. He covered a part of the distance on foot at the rate of 4 km per hour and a part on a bicycle at the rate of 10 km per hour. How much distance (in km) did he travel on foot?
  • a)
    10 km
  • b)
    20 km
  • c)
    30 km
  • d)
    40 km
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A person travelled a distance of 50 km in 8 hours. He covered a part o...
To solve this problem, we can use the formula:

Distance = Rate × Time

Let's assume that the person traveled x km on foot and (50 - x) km on a bicycle.

On foot:
Distance = Rate × Time
x = 4 km/hr × t1 (where t1 is the time taken on foot)

On a bicycle:
Distance = Rate × Time
50 - x = 10 km/hr × t2 (where t2 is the time taken on a bicycle)

We are given that the total time taken is 8 hours. So we can write the equation:

t1 + t2 = 8

Now, we need to solve these two equations simultaneously to find the values of x, t1, and t2.

1. Solve equation 1 for t1:
x = 4t1

2. Solve equation 2 for t2:
50 - x = 10t2
x = 50 - 10t2

3. Substitute the value of x from equation 1 into equation 2:
4t1 = 50 - 10t2

4. Rearrange the equation:
10t2 + 4t1 = 50

5. Rewrite the equation in terms of t1:
5t2 + 2t1 = 25

6. Rearrange the equation:
2t1 = 25 - 5t2

7. Substitute the value of t1 from equation 5 into equation 6:
2(25 - 5t2) = 25 - 5t2

8. Simplify the equation:
50 - 10t2 = 25 - 5t2

9. Combine like terms:
5t2 = 25

10. Divide both sides by 5:
t2 = 5

11. Substitute the value of t2 into equation 5:
5(5) + 2t1 = 25

12. Simplify the equation:
25 + 2t1 = 25

13. Subtract 25 from both sides:
2t1 = 0

14. Divide both sides by 2:
t1 = 0

Since t1 represents the time taken on foot, and we know that time cannot be zero, we can conclude that the person did not travel any distance on foot.

Therefore, the person traveled 50 km on a bicycle and 0 km on foot. The answer is option B, 20 km.
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Community Answer
A person travelled a distance of 50 km in 8 hours. He covered a part o...
Given:
Time taken to cover 50 km is 8 hours
Speed on his foot is 4 km/h
Speed on bicycle is 10 km/h
Formula used:
Speed = Distance/Time
Calculation:
Let the distance covered on foot be x km
Distance covered by bicycle is (50 - x) km
According to question
⇒ x/4 + (50 - x)/10 = 8
⇒ (5x + 100 - 2x)/20 = 8
⇒ 3x + 100 = 160
⇒ 3x = 60
⇒ x = 20 km
∴ The distance travelled on foot is 20 km.
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Direction: Read the following passage carefully and answer the given questions.Once upon a time, there was a greedy merchant who owned a magnificent horse. The horse was strong and fast, and the merchant was proud of it. He would often travel long distances with the horse to trade goods and make a profit.One day, the merchant had to travel to a faraway city to sell his goods. He decided to take his horse with him as he knew it could cover the distance quickly. However, he didnt consider the fact that the horse would need rest and care along the way.As they started their journey, the merchant pushed the horse to go faster and faster, not stopping for breaks. The horse was getting tired and was unable to keep up with the merchants demands. The merchant didnt care and continued to ride the horse harder, thinking only of his profit.As they travelled further, the horse began to slow down, and its breathing became laboured. The merchant didnt take notice and kept pushing the horse until it eventually collapsed on the ground, exhausted and unable to move.The merchant was angry and frustrated that his horse had failed him. He cursed the animal and tried to force it to get up, but the horse was too weak to move. Realizing that he wouldnt be able to reach his destination without a horse, the merchant decided to leave the animal behind and continue on foot, leaving the exhausted horse on the side of the road.Days later, the merchant finally reached his destination, but he had lost a lot of his merchandise along the way. He realized that his greed had led to his downfall, and he regretted his actions towards the horse. He wished he had taken better care of it and had considered its needs.From that day on, the merchant vowed to treat his animals with kindness and respect and not to let his greed get in the way of his morals. The lesson he learned was that sometimes, taking a break and looking after yourself and those around you is more important than making a profit.Q.Why merchant travel long distances with his horse?

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A person travelled a distance of 50 km in 8 hours. He covered a part of the distance on foot at the rate of 4 km per hour and a part on a bicycle at the rate of 10 km per hour. How much distance (in km) did he travel on foot?a)10 kmb)20 kmc)30 kmd)40 kmCorrect answer is option 'B'. Can you explain this answer?
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