Quantitative Aptitude is an equally important section for SSC CGL, CHSL, MTS exams and has an even more abundant importance in some other exams conducted by SSC. Generally, there are questions asked related to basic concepts and formulas of Time Speed And Distance.
To let you make the most of QUANT section, we are providing important facts related to Circle. Also, Railway Exam is nearby with bunches of posts for the interested candidates in which quantitative aptitude is a major part. We have covered important notes and questions focusing on these prestigious exams. We wish you all the best of luck to come over the fear of Mathematics section.
Time Speed & Distance
Distance = Time × Speed
- When Distance is constant
Time ∝ 1/speed
- When Time is constant
Distance ∝ speed
- When speed in constant
Distance ∝ Time
- Average speed = (Total Distance )/(Total Time Taken)
- When Distance is equal
Average speed = 2xy/(x + y)
x, y → speeds
Q1. A car takes half of the time taken by truck to go from Lucknow to Bombay. A truck takes 20 hours to go for the same journey. What is the speed of truck, if the speed of car be 120 km/hr?
Q2. Shweta when increases her speed from 24 km/hr to 30 km/hr she takes one hour less than the usual time to cover a certain distance. What is the distance usually covered by Shweta?
Q3. Kriplani goes to school at 20 km/hr and reaches the school 4 minutes late. Next time, she goes at 25 km/hr and reaches the school 2 minutes earlier than the scheduled time. What is the distance of her school?
Q4. Udai travels half of his journey by train at the speed of 120 km/hr and rest half by car at 80 km/hr. What is the average speed?
Q5. Walking at 4/5 of his normal speed, Dewang is 15 minutes late in reaching his club. What is the usual time taken by him to cover the distance?
Relative Speed→
a) When two bodies move in the same direction, Let speed of two bodies be S₁ & S₂.
Relative speed = S₁ – S₂
(b) When two bodies are moving in the opposite direction. Let the speed of two bodies be S₁ & S₂.
Relative speed = S₁ + S₂.
(c) When two bodies moving towards each other than time taken by them to meet.
D → Distance between two bodies.
S₁, S₂ → Speed of two bodies.
T, time taken to meet other = D/(S₁ + S₂ )
(d) When two bodies are moving in opposite direction, time taken to meet.
D→ Distance between the two bodies.
S₁, S₂ → Speed of two bodies.
T, time taken = D/(S₁ – S₂ )
(e) If two persons A & B, start at the same time from P and Q towards each other and after crossing they take T₁ & T₂ hrs in reaching Q & P
S₁ /S₂ =√(T₁/T₂ )
Q1. The distance between 2 places R and S is 42 km. Anita starts from R with a uniform speed of 4 km/hr towards S and at the same time Romita starts from S towards R also with some uniform speed. They meet each other after 6 hours. The speed of Romita is
Q2. The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 km/hr. At what time do they meet?
Q3. A thief Bhagu Ram is spotted by the policeman Pakad Singh from a distance of 200m. Once they see each other they start Running. What is the distance Bhagu Ram, who is running at 5 km/hr would have covered before being caught by Pakad Singh running at 7 km/hr?
Q4. A train starts from A to B at 9:00 am and takes 6 hours to travel to B. Another train starts from B to A at 10:00 am and takes 8 hours to travel to A. At what time both train will meet?
Q5. Abhinav leaves Mumbai at 6 am and reaches Bangalore at 10 am Praveen leaves Bangalore at 8 am and reaches Mumbai at 11:30 am. At what time do they cross each other?
Trains
(a) If a train of length l meters passes a platform or bridge of length m metres, then distance travelled is
Distance = l + m
(b) If a train of length l meters passes a pole, man, tree etc, then Distance travelled is
Distance = l meters
(c) If two trains of lengths L₁ & L₂ are travelling in the same direction with speeds S₁ & S₂ then. Time taken by faster train to cross slower train is given by
T=(L₁+L₂)/(S₁-S₂)
(d) If two trains of length L₁ & L₂ are travelling is opposite direction with speeds S₁ & S₂, then time taken by trains to cross each other is
T=(L₁+L₂)/(S₁-S₂)
(e) Two trains of length L₁ & L₂ run on parallel tracks. When running is same direction, the faster train passes slower train in T₁ secs, but when they are running in opposite direction with same speeds, they passes each other in T₂ sec. Then,
Q1. Two trains of length 200 m and 175 m run or parallel tracks. When running is the same direction the faster train crosses the slower train in 37½ sec. While running is opposite directions they passes each other is 7½ s. Find the speed of each train.
Q2. A train crosses a man coming from the opposite direction in 7.5 seconds. If the speed of man be 10 m/s and speed of train is 20 m/s, find the length of the train.
Q3. Two trains coming from the opposite sides crosses each other in 10 seconds if the lengths of first train and second train be 125 m and 175 m respectively, also the speed of first train be 36 km/hr, find the speed of second train.
Q4. A train overtakes two girls who are walking in the opposite direction in which the train is going at the rate of 3 km/hr and 6 km/hr and passes them completely in 36 seconds and 30 seconds respectively. The length of the train (in metres) is:
Boat & Stream
(a) Downstream→ When boat & stream moves in the same direction.
Downstream Speed = u + v
u → speed of boat
v → speed of stream
(b) Upstream→ When boat & stream moves in the opposite direction.
Upstream speed = u – v
u → speed of boat
v → speed of stream
(c) If D → is downstream speed , U→ is upstream speed.Then,
Speed of boat = (D + U)/2
Speed of stream = (D – U)/2
(d) When the distance traveled by boat is downstream is same as the distance covered by boat is upstream, then,
Q1. A man can row 9 km/hr in still water. If takes him twice as long as to row up as to row down. Find the rate of stream of river.
Q2. The speed of a boat downstream is 15 km/hr and the speed of current is 3 km/hr. Find the total time taken by the boat to cover 15 km upstream and 15 km downstream.
Q3. A man rows 12 km in 5 hours against the stream and the speed of current being 4 kmph. What time will be taken by him to row 15 km with the stream?
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