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P can do a work in the same time in which Q and R together can do it. If P and Q work together, the work can be completed in 10 days. R alone needs 50 days to complete the same work. then Q alone can do it in
- a)30 days
- b)25 days
- c)20 days
- d)15 days
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
P can do a work in the same time in which Q and R together can do it. ...
Work done by P and Q in 1 day = 1/10
Work done by R in 1 day = 1/50
Work done by P, Q and R in 1 day = 1/10 + 1/50 = 6/50
But Work done by P in 1 day = Work done by Q and R in 1 day . Hence the above equation can be written as
Work done by P in 1 day * 2 = 6/50
=> Work done by P in 1 day = 3/50
=> Work done by Q and R in 1 day = 3/50
Hence work done by Q in 1 day = 3/50 – 1/50 = 2/50 = 1/25
So Q alone can do the work in 25 days
Most Upvoted Answer
P can do a work in the same time in which Q and R together can do it. ...
Let distance between the two places = d km
Let total time taken by faster horse = t hr
⇒ Total time taken by slower horse = (t + 5) hr,
Let total time taken by faster horse = t hr
⇒ Total time taken by slower horse = (t + 5) hr,
Therefore,
speed of the faster horse = d/t km/hr
speed of the slower horse = d/(t + 5) km/hr
The two horses meet each other in 3 hour 20 min i.e. in 3(1/3) hr = 10/3 hr
In this time, total distance travelled by both the horses together is d.
speed of the faster horse = d/t km/hr
speed of the slower horse = d/(t + 5) km/hr
The two horses meet each other in 3 hour 20 min i.e. in 3(1/3) hr = 10/3 hr
In this time, total distance travelled by both the horses together is d.
∴ d/(t+5) * 10/3 + d/t * 10/3 = d
⇒ 10/(3(t+5)) + 10/3t = 1
⇒ 10t + 10(t+5) = 3t(t+5)
⇒ 20t + 50 = 3t2 + 15t
⇒ 3t2 − 5t − 50 = 0
⇒ 3t2 + 10t − 15t − 50 = 0
⇒ t(3t + 10) − 5(3t + 10) = 0
⇒ (3t + 10)(t − 5) = 0
⇒ t = 5 (ignoring -ve value)
⇒ 10/(3(t+5)) + 10/3t = 1
⇒ 10t + 10(t+5) = 3t(t+5)
⇒ 20t + 50 = 3t2 + 15t
⇒ 3t2 − 5t − 50 = 0
⇒ 3t2 + 10t − 15t − 50 = 0
⇒ t(3t + 10) − 5(3t + 10) = 0
⇒ (3t + 10)(t − 5) = 0
⇒ t = 5 (ignoring -ve value)
Thus, Total time taken by slower horse = 5 + 5 = 10 hr
So Option B is correct
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Community Answer
P can do a work in the same time in which Q and R together can do it. ...
Given:
- Two cars started simultaneously towards each other and met each other 3 h 20 min later.
- The first arrived at the place of departure of the second 5 hours later than the second arrived at the point of departure of the first.
To Find: How much time will it take the slower car to cover the whole distance.
Let's assume:
- The distance between the two cars is 'd'.
- The speed of the faster car is 'x' km/hr.
- The speed of the slower car is 'y' km/hr.
Calculations:
- As both cars started simultaneously towards each other, the relative speed between them is (x+y) km/hr.
- They met each other 3 h 20 min later, which is 10/3 hours.
- Therefore, the total distance covered by both cars = (x+y) * 10/3 = 10(x+y)/3 km.
- Let's assume the slower car covered the distance 'd' in 't' hours.
- So, the faster car covered the distance 'd' in (t-5) hours.
- Distance = Speed * Time
- Therefore, d = y * t (for the slower car) and d = x * (t-5) (for the faster car)
- From the above equations, we can equate both distances, i.e. y * t = x * (t-5)
- Solving the above equation, we get t = 10 hours.
Therefore, the slower car took 10 hours to cover the whole distance. Hence, the correct answer is option 'B'.
- Two cars started simultaneously towards each other and met each other 3 h 20 min later.
- The first arrived at the place of departure of the second 5 hours later than the second arrived at the point of departure of the first.
To Find: How much time will it take the slower car to cover the whole distance.
Let's assume:
- The distance between the two cars is 'd'.
- The speed of the faster car is 'x' km/hr.
- The speed of the slower car is 'y' km/hr.
Calculations:
- As both cars started simultaneously towards each other, the relative speed between them is (x+y) km/hr.
- They met each other 3 h 20 min later, which is 10/3 hours.
- Therefore, the total distance covered by both cars = (x+y) * 10/3 = 10(x+y)/3 km.
- Let's assume the slower car covered the distance 'd' in 't' hours.
- So, the faster car covered the distance 'd' in (t-5) hours.
- Distance = Speed * Time
- Therefore, d = y * t (for the slower car) and d = x * (t-5) (for the faster car)
- From the above equations, we can equate both distances, i.e. y * t = x * (t-5)
- Solving the above equation, we get t = 10 hours.
Therefore, the slower car took 10 hours to cover the whole distance. Hence, the correct answer is option 'B'.
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P can do a work in the same time in which Q and R together can do it. If P and Q work together, the work can be completed in 10 days. R alone needs 50 days to complete the same work. then Q alone can do it ina)30 days b)25 daysc)20 daysd)15 daysCorrect answer is option 'B'. Can you explain this answer?
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