IPMPrepA car goes from P to Q at 30 km/h and returns at 72 km/h. What is its average speed for the round trip?
Solution
For equal distances, average speed = 2ab/(a + b).
= 2 × 30 × 72102 = 72017 km/h.
Answer: (C) 72017 km/h
Quantitative Ability · Arithmetic
Time, Speed and Distance: IPMAT practice questions
24 questions. Each is marked with the exam level it suits. Answer, then open the step-by-step solution.
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A boat's speed in still water is 8 km/h and the stream flows at 4 km/h. How long does it take to go 12 km downstream and come back?
Solution
Downstream speed = 12 km/h; upstream = 4 km/h.
Time = 1212 + 124 = 4 hours.
Answer: (A) 4 hours
Towns X and Y are 200 km apart. A car leaves X for Y at 35 km/h; 1 hour later another car leaves Y for X at 64 km/h. How far from X do they meet?
Solution
In the first 1 h the first car covers 35 km, leaving 165 km.
They then close the gap at 99 km/h: time = 16599 = 1 23 h.
Distance from X = 35 × (1 + 1 23) = 93 13 km.
Answer: (C) 93 13 km
Two runners start together from the same point of a 800 m circular track at 4 m/s and 6 m/s, running in opposite directions. After how many seconds do they first meet again at the starting point?
Solution
Lap times: 200 s and 133 13 s.
They are together at the start after the LCM of the lap times: 400 s.
Answer: (D) 400 s
Walking at 7 km/h a student reaches school 20 minutes late; at 10 km/h he is 7 minutes early. How far is the school?
Solution
The two times differ by 27 minutes = 920 h.
d/7 − d/10 = 920, so d × 370 = 920.
d = 10.5 km.
Answer: (D) 10.5 km
Two trains 100 m and 270 m long run at 54 km/h and 36 km/h in the same direction. How long do they take to cross each other completely?
Solution
Relative speed = 18 km/h = 5 m/s.
Distance = 100 + 270 = 370 m.
Time = 370 ÷ 5 = 74 s.
Answer: (D) 74 seconds
Walking at 9 km/h a student reaches school 17 minutes late; at 10 km/h he is 11 minutes early. How far is the school?
Solution
The two times differ by 28 minutes = 715 h.
d/9 − d/10 = 715, so d × 190 = 715.
d = 42 km.
Answer: (B) 42 km
A car goes from P to Q at 78 km/h and returns at 75 km/h. What is its average speed for the round trip?
Solution
For equal distances, average speed = 2ab/(a + b).
= 2 × 78 × 75153 = 130017 km/h.
Answer: (C) 130017 km/h
A boat's speed in still water is 20 km/h and the stream flows at 5 km/h. How long does it take to go 75 km downstream and come back?
Solution
Downstream speed = 25 km/h; upstream = 15 km/h.
Time = 7525 + 7515 = 8 hours.
Answer: (A) 8 hours
Towns X and Y are 350 km apart. A car leaves X for Y at 49 km/h; 2 hours later another car leaves Y for X at 63 km/h. How far from X do they meet?
Solution
In the first 2 h the first car covers 98 km, leaving 252 km.
They then close the gap at 112 km/h: time = 252112 = 2.25 h.
Distance from X = 49 × (2 + 2.25) = 208.25 km.
Answer: (A) 208.25 km
Towns X and Y are 180 km apart. A car leaves X for Y at 40 km/h and at the same time another car leaves Y for X at 32 km/h. How far from X do they meet?
Solution
They then close the gap at 72 km/h: time = 18072 = 2.5 h.
Distance from X = 40 × 2.5 = 100 km.
Answer: (B) 100 km
Walking at 4 km/h a student reaches school 7 minutes late; at 6 km/h he is 8 minutes early. How far is the school?
Solution
The two times differ by 15 minutes = 14 h.
d/4 − d/6 = 14, so d × 112 = 14.
d = 3 km.
Answer: (D) 3 km
Two runners start together from the same point of a 1200 m circular track at 4 m/s and 10 m/s, running in opposite directions. When do they first meet?
Solution
Relative speed = 14 m/s; the gap to close is one lap of 1200 m.
Time = 120014 = 85 57 s.
Answer: (C) 85 57 s
Two runners start together from the same point of a 600 m circular track at 3 m/s and 5 m/s, running in the same direction. After how many seconds do they first meet again at the starting point?
Solution
Lap times: 200 s and 120 s.
They are together at the start after the LCM of the lap times: 600 s.
Answer: (D) 600 s
Walking at 8 km/h a student reaches school 13 minutes late; at 9 km/h he is 7 minutes early. How far is the school?
Solution
The two times differ by 20 minutes = 13 h.
d/8 − d/9 = 13, so d × 172 = 13.
d = 24 km.
Answer: (A) 24 km
A car goes from P to Q at 56 km/h and returns at 40 km/h. What is its average speed for the round trip?
Solution
For equal distances, average speed = 2ab/(a + b).
= 2 × 56 × 4096 = 46 23 km/h.
Answer: (B) 46 23 km/h
A boat's speed in still water is 8 km/h and the stream flows at 3 km/h. How long does it take to go 110 km downstream and come back?
Solution
Downstream speed = 11 km/h; upstream = 5 km/h.
Time = 11011 + 1105 = 32 hours.
Answer: (C) 32 hours
Two trains 280 m and 290 m long run at 36 km/h and 72 km/h towards each other. How long do they take to cross each other completely?
Solution
Relative speed = 108 km/h = 30 m/s.
Distance = 280 + 290 = 570 m.
Time = 570 ÷ 30 = 19 s.
Answer: (A) 19 seconds
Two trains 110 m and 160 m long run at 72 km/h and 36 km/h towards each other. How long do they take to cross each other completely?
Solution
Relative speed = 108 km/h = 30 m/s.
Distance = 110 + 160 = 270 m.
Time = 270 ÷ 30 = 9 s.
Answer: (C) 9 seconds
A car goes from P to Q at 28 km/h and returns at 35 km/h. What is its average speed for the round trip?
Solution
For equal distances, average speed = 2ab/(a + b).
= 2 × 28 × 3563 = 31 19 km/h.
Answer: (A) 31 19 km/h
Towns X and Y are 160 km apart. A car leaves X for Y at 36 km/h; 1 hour later another car leaves Y for X at 57 km/h. How far from X do they meet?
Solution
In the first 1 h the first car covers 36 km, leaving 124 km.
They then close the gap at 93 km/h: time = 12493 = 1 13 h.
Distance from X = 36 × (1 + 1 13) = 84 km.
Answer: (A) 84 km
Two trains 120 m and 190 m long run at 36 km/h and 45 km/h in the same direction. How long do they take to cross each other completely?
Solution
Relative speed = 9 km/h = 2.5 m/s.
Distance = 120 + 190 = 310 m.
Time = 310 ÷ 2.5 = 124 s.
Answer: (D) 124 seconds
Two runners start together from the same point of a 800 m circular track at 6 m/s and 9 m/s, running in opposite directions. After how many seconds do they first meet again at the starting point?
Solution
Lap times: 133 13 s and 88 89 s.
They are together at the start after the LCM of the lap times: 266 23 s.
Answer: (C) 266 23 s
A boat's speed in still water is 18 km/h and the stream flows at 3 km/h. How long does it take to go 105 km downstream and come back?
Solution
Downstream speed = 21 km/h; upstream = 15 km/h.
Time = 10521 + 10515 = 12 hours.
Answer: (D) 12 hours
These are original practice questions written by Target Campus in the pattern, syllabus and difficulty of IPMAT Indore, IPMAT Rohtak, JIPMAT, NPAT and SET. They are not previous-year papers.