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The Sinhagad Express left Pune at noon sharp. Two hours later, the Deccan Queen started from Pune in the same direction. The Deccan Queen overtook the Sinhagad Express at 8 p.m. Find the average speed of the two trains over this journey if the sum of their average speeds is 70 km/h.
- a)34.28 km/h
- b)35 km/h
- c)50 km/h
- d)12 km/h
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The Sinhagad Express left Pune at noon sharp. Two hours later, the Dec...
The ratio of time for the travel is 4:3 (Sinhagad to Deccan Queen). Hence, the ratio of speeds
would be 3:4. Since, the sum of their average speeds is 70 kmph, their respective speeds would
be 30 and 40 kmph respectively. Use alligation to get the answer as 34.28 kmph.
would be 3:4. Since, the sum of their average speeds is 70 kmph, their respective speeds would
be 30 and 40 kmph respectively. Use alligation to get the answer as 34.28 kmph.
Most Upvoted Answer
The Sinhagad Express left Pune at noon sharp. Two hours later, the Dec...
Given data:
- Sinhagad Express started from Pune at noon sharp.
- Deccan Queen started from Pune in the same direction two hours later.
- Deccan Queen overtook Sinhagad Express at 8 p.m.
To find:
- Average speed of the two trains over this journey.
Approach:
- Let the average speed of Sinhagad Express be x km/h.
- Therefore, the average speed of Deccan Queen will be (70 - x) km/h (given sum of their average speeds is 70 km/h).
- Let the distance travelled by Sinhagad Express in 8 hours (from noon to 8 p.m.) be d1 km.
- Therefore, the distance travelled by Deccan Queen in 6 hours (from 2 p.m. to 8 p.m.) will also be d1 km (because it overtook Sinhagad Express).
- Let the total distance between Pune and the point where Deccan Queen overtook Sinhagad Express be d km.
- Therefore, the distance travelled by Sinhagad Express in the first 6 hours (from noon to 6 p.m.) will be (d - d1) km.
- Now, we can use the formula: distance = speed × time to form two equations and solve them simultaneously to get the value of x.
Calculation:
- Distance travelled by Sinhagad Express in the first 6 hours = (d - d1) km
- Time taken by Sinhagad Express to cover this distance = 6 hours
- Therefore, x = (d - d1) / 6
- Distance travelled by Deccan Queen in 6 hours = d1 km
- Time taken by Deccan Queen to cover this distance = 6 hours
- Therefore, (70 - x) = d1 / 6
- Adding the above two equations, we get:
70 = d / 6
d = 420 km
- Substituting the value of d in the above equations, we get:
x = 28 km/h
(70 - x) = 42 km/h
- Therefore, the average speed of the two trains over this journey will be:
(2xd) / (8 hours) = (2 × 420) / 8 = 84 / 4 = 21 km/h
- But we need to find the average speed of the two trains together, which will be:
(average speed of Sinhagad Express + average speed of Deccan Queen) / 2
= (28 + 42) / 2 = 70 / 2 = 35 km/h
Therefore, option (A) 34.28 km/h is incorrect and the correct answer is option (B) 35 km/h.
- Sinhagad Express started from Pune at noon sharp.
- Deccan Queen started from Pune in the same direction two hours later.
- Deccan Queen overtook Sinhagad Express at 8 p.m.
To find:
- Average speed of the two trains over this journey.
Approach:
- Let the average speed of Sinhagad Express be x km/h.
- Therefore, the average speed of Deccan Queen will be (70 - x) km/h (given sum of their average speeds is 70 km/h).
- Let the distance travelled by Sinhagad Express in 8 hours (from noon to 8 p.m.) be d1 km.
- Therefore, the distance travelled by Deccan Queen in 6 hours (from 2 p.m. to 8 p.m.) will also be d1 km (because it overtook Sinhagad Express).
- Let the total distance between Pune and the point where Deccan Queen overtook Sinhagad Express be d km.
- Therefore, the distance travelled by Sinhagad Express in the first 6 hours (from noon to 6 p.m.) will be (d - d1) km.
- Now, we can use the formula: distance = speed × time to form two equations and solve them simultaneously to get the value of x.
Calculation:
- Distance travelled by Sinhagad Express in the first 6 hours = (d - d1) km
- Time taken by Sinhagad Express to cover this distance = 6 hours
- Therefore, x = (d - d1) / 6
- Distance travelled by Deccan Queen in 6 hours = d1 km
- Time taken by Deccan Queen to cover this distance = 6 hours
- Therefore, (70 - x) = d1 / 6
- Adding the above two equations, we get:
70 = d / 6
d = 420 km
- Substituting the value of d in the above equations, we get:
x = 28 km/h
(70 - x) = 42 km/h
- Therefore, the average speed of the two trains over this journey will be:
(2xd) / (8 hours) = (2 × 420) / 8 = 84 / 4 = 21 km/h
- But we need to find the average speed of the two trains together, which will be:
(average speed of Sinhagad Express + average speed of Deccan Queen) / 2
= (28 + 42) / 2 = 70 / 2 = 35 km/h
Therefore, option (A) 34.28 km/h is incorrect and the correct answer is option (B) 35 km/h.
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The Sinhagad Express left Pune at noon sharp. Two hours later, the Deccan Queen started from Pune in the same direction. The Deccan Queen overtook the Sinhagad Express at 8 p.m. Find the average speed of the two trains over this journey if the sum of their average speeds is 70 km/h.a)34.28 km/hb)35 km/hc)50 km/hd)12 km/hCorrect answer is option 'A'. Can you explain this answer?
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The Sinhagad Express left Pune at noon sharp. Two hours later, the Deccan Queen started from Pune in the same direction. The Deccan Queen overtook the Sinhagad Express at 8 p.m. Find the average speed of the two trains over this journey if the sum of their average speeds is 70 km/h.a)34.28 km/hb)35 km/hc)50 km/hd)12 km/hCorrect answer is option 'A'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The Sinhagad Express left Pune at noon sharp. Two hours later, the Deccan Queen started from Pune in the same direction. The Deccan Queen overtook the Sinhagad Express at 8 p.m. Find the average speed of the two trains over this journey if the sum of their average speeds is 70 km/h.a)34.28 km/hb)35 km/hc)50 km/hd)12 km/hCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The Sinhagad Express left Pune at noon sharp. Two hours later, the Deccan Queen started from Pune in the same direction. The Deccan Queen overtook the Sinhagad Express at 8 p.m. Find the average speed of the two trains over this journey if the sum of their average speeds is 70 km/h.a)34.28 km/hb)35 km/hc)50 km/hd)12 km/hCorrect answer is option 'A'. Can you explain this answer?.
The Sinhagad Express left Pune at noon sharp. Two hours later, the Deccan Queen started from Pune in the same direction. The Deccan Queen overtook the Sinhagad Express at 8 p.m. Find the average speed of the two trains over this journey if the sum of their average speeds is 70 km/h.a)34.28 km/hb)35 km/hc)50 km/hd)12 km/hCorrect answer is option 'A'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The Sinhagad Express left Pune at noon sharp. Two hours later, the Deccan Queen started from Pune in the same direction. The Deccan Queen overtook the Sinhagad Express at 8 p.m. Find the average speed of the two trains over this journey if the sum of their average speeds is 70 km/h.a)34.28 km/hb)35 km/hc)50 km/hd)12 km/hCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The Sinhagad Express left Pune at noon sharp. Two hours later, the Deccan Queen started from Pune in the same direction. The Deccan Queen overtook the Sinhagad Express at 8 p.m. Find the average speed of the two trains over this journey if the sum of their average speeds is 70 km/h.a)34.28 km/hb)35 km/hc)50 km/hd)12 km/hCorrect answer is option 'A'. Can you explain this answer?.
Solutions for The Sinhagad Express left Pune at noon sharp. Two hours later, the Deccan Queen started from Pune in the same direction. The Deccan Queen overtook the Sinhagad Express at 8 p.m. Find the average speed of the two trains over this journey if the sum of their average speeds is 70 km/h.a)34.28 km/hb)35 km/hc)50 km/hd)12 km/hCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
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