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From his home, Rahul walks 6/7 km towards school and then returns 5/6 km on the same way towards his home to reach a landmark. Where will he be now from his home?
- a)1/42 km
- b)42 km
- c)30 km
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Problem:
Rahul walks 6/7 km towards school from his home and then returns 5/6 km on the same way towards his home to reach a landmark. Where will he be now from his home?
Solution:
To find out where Rahul will be now from his home, we need to calculate the net distance covered by him.
Step 1: Calculating the distance towards the school
Rahul walks 6/7 km towards the school from his home. This means he walks 6/7 of a kilometer in one direction.
Step 2: Calculating the distance towards home
After reaching the school, Rahul returns 5/6 km towards his home. This means he walks 5/6 of a kilometer in the opposite direction.
Step 3: Calculating the net distance
To find the net distance covered by Rahul, we need to subtract the distance towards home from the distance towards the school.
Net distance = Distance towards school - Distance towards home
Net distance = 6/7 km - 5/6 km
Step 4: Finding the common denominator
To subtract fractions, we need to find a common denominator. In this case, the least common multiple (LCM) of 7 and 6 is 42.
Step 5: Converting the fractions
We need to convert the fractions to have the same denominator of 42.
6/7 km = (6/7) * (6/6) km = 36/42 km
5/6 km = (5/6) * (7/7) km = 35/42 km
Now we can subtract the fractions:
Net distance = 36/42 km - 35/42 km = (36 - 35)/42 km = 1/42 km
Conclusion:
After walking towards the school and then returning towards home, Rahul will be 1/42 km away from his home. Therefore, the correct answer is option 'A' - 1/42 km.
Rahul walks 6/7 km towards school from his home and then returns 5/6 km on the same way towards his home to reach a landmark. Where will he be now from his home?
Solution:
To find out where Rahul will be now from his home, we need to calculate the net distance covered by him.
Step 1: Calculating the distance towards the school
Rahul walks 6/7 km towards the school from his home. This means he walks 6/7 of a kilometer in one direction.
Step 2: Calculating the distance towards home
After reaching the school, Rahul returns 5/6 km towards his home. This means he walks 5/6 of a kilometer in the opposite direction.
Step 3: Calculating the net distance
To find the net distance covered by Rahul, we need to subtract the distance towards home from the distance towards the school.
Net distance = Distance towards school - Distance towards home
Net distance = 6/7 km - 5/6 km
Step 4: Finding the common denominator
To subtract fractions, we need to find a common denominator. In this case, the least common multiple (LCM) of 7 and 6 is 42.
Step 5: Converting the fractions
We need to convert the fractions to have the same denominator of 42.
6/7 km = (6/7) * (6/6) km = 36/42 km
5/6 km = (5/6) * (7/7) km = 35/42 km
Now we can subtract the fractions:
Net distance = 36/42 km - 35/42 km = (36 - 35)/42 km = 1/42 km
Conclusion:
After walking towards the school and then returning towards home, Rahul will be 1/42 km away from his home. Therefore, the correct answer is option 'A' - 1/42 km.
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