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Two men together start a journey in the same direction. They travel 12 and 20 km/day respectively. After travelling for 8 days the man travelling at 12 km/day doubles his speed and both finish the distance in the same time. Find the number of days taken by them to reach the destination.
- a)28 days
- b)26 days
- c)24 days
- d)30 days
- e)22 days
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Two men together start a journey in the same direction. They travel 12...
For distance,
Distance travelled in 8 days by 1st man,
D1 = 12 × 8 = 96 km.
and by 2nd man,
D2 = 20 × 8 = 160 km
For remaining distance, let both take t days
to reach the destination.
x – 96 = 2 × 12 × t
x – 96 = 24 t .......... (i)
and x – 160 = 20 t ...... (ii)
From (i) and (ii); we get,
x – 96 – x + 160 = 24 t – 20 t
64 = 4 t
t = 16 days.
Total number of days = 16 + 8 = 24 days.
Most Upvoted Answer
Two men together start a journey in the same direction. They travel 12...
Problem: Two men start a journey in the same direction. They travel 12 and 20 km/day respectively. After travelling for 8 days the man travelling at 12 km/day doubles his speed and both finish the distance in the same time. Find the number of days taken by them to reach the destination.
Solution: Let the distance to be covered be D km. Let the second man take x days to cover the distance.
Initial distance covered by the first man = 12 x 8 = 96 km
Initial distance covered by the second man = 20 x 8 = 160 km
Let the speed of the first man after 8 days be v km/day. Then, the remaining distance covered by the first man = (D - 96) km.
As per the given condition, both men finish the distance in the same time. So, we can equate the time taken by both men to cover the remaining distance.
Time taken by the first man to cover the remaining distance = (D - 96)/v
Time taken by the second man to cover the entire distance = D/20
As per the given condition, both times are equal. So, we get the following equation:
(D - 96)/v = D/20
Solving for D, we get D = 960 km.
Now, we can use the distance formula to find the time taken by both men to cover the distance.
For the first man, time taken = (96 + (D - 96) / 2)/12
For the second man, time taken = D/40 + x
As per the given condition, both times are equal. So, we get the following equation:
(96 + (D - 96) / 2)/12 = D/40 + x
Substituting the value of D, we get x = 16.
So, the total number of days taken by both men to cover the distance = 8 + 16 = 24.
Therefore, the correct option is (c) 24 days.
Solution: Let the distance to be covered be D km. Let the second man take x days to cover the distance.
Initial distance covered by the first man = 12 x 8 = 96 km
Initial distance covered by the second man = 20 x 8 = 160 km
Let the speed of the first man after 8 days be v km/day. Then, the remaining distance covered by the first man = (D - 96) km.
As per the given condition, both men finish the distance in the same time. So, we can equate the time taken by both men to cover the remaining distance.
Time taken by the first man to cover the remaining distance = (D - 96)/v
Time taken by the second man to cover the entire distance = D/20
As per the given condition, both times are equal. So, we get the following equation:
(D - 96)/v = D/20
Solving for D, we get D = 960 km.
Now, we can use the distance formula to find the time taken by both men to cover the distance.
For the first man, time taken = (96 + (D - 96) / 2)/12
For the second man, time taken = D/40 + x
As per the given condition, both times are equal. So, we get the following equation:
(96 + (D - 96) / 2)/12 = D/40 + x
Substituting the value of D, we get x = 16.
So, the total number of days taken by both men to cover the distance = 8 + 16 = 24.
Therefore, the correct option is (c) 24 days.
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Two men together start a journey in the same direction. They travel 12 and 20 km/day respectively. After travelling for 8 days the man travelling at 12 km/day doubles his speed and both finish the distance in the same time. Find the number of days taken by them to reach the destination.a)28 daysb)26 daysc)24 daysd)30 dayse)22 daysCorrect answer is option 'C'. Can you explain this answer?
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