Quantitative Aptitude Study Notes
Bank & SSC
Exam
TIME AND DISTANCE
You know that quantitative
aptitude section is most important in bank
exams in PO and Clerk and for
other competitive exams because if you want good score in bank exam then you
have to score good in maths. In competitive exams the most important thing is
time management, if you know how to manage your time then you can do well in Bank Exams. That’s where maths shortcut
tricks and formula are comes into action. So continuously we are providing
shortcut tricks on different maths topics.
Today’s topic is TIME AND DISTANCE. This is the one of the most important topic in quantitative
aptitude section in bank and ssc exam. You should know how to calculate time
and distance questions and answers in very short time for bank exam. From this
chapter around 1-2 questions are given in the SBI and IBPS exams. For this here we are providing shortcut tricks
and quicker method to calculate time and distance in very short time.
If we want to solve time and
distance questions or any other type of questions, then the first thing that we
need that is Formulas about that topic. So here is the list of formulas that is
used in time and distance quantitative topic.
i.
SPEED = DISTANCE / TIME
ii.
TIME = DISTANCE / SPEED
iii.
DISTANCE = SPEED × TIME
iv.
If the speed of a body is changed
in the ratio a:b, then the ratio of the time taken changes in the ratio b:a
v.
x km/hr = (x × 5/18) m/sec.
vi.
X meters/sec = (x × 18/5) km/hr.
EXAMPLE 1: Express a speed of 18 km/hr in
meters per second.
Solution: 18 km/hr = ( 18 × 5/18) m/sec =
5 meters/sec.
EXAPMLE 2: Express 10 m/sec in km/hr.
Solution: 10m/sec = (10 × 18/5) km/hr = 36
km/hr.
Theorem: if a certain distance is covered
at x km/hr and the same distance is covered at y km/hr then the average speed
during the whole journey is 2xy/x+y km/hr.
Proof:
let the distance be A km. Time taken to travel the distance at a speed of x
km/hr = A/x hrs.
Time
taken to travel the distance at a speed of y km/hr = A/y hrs.
Thus,
we see that the total distance of 2A km is travelled in (A/x + A/y) hrs.
AVERAGE SPEED =
Solution: Average speed = 2 * 70 * 55 / 70
+ 55 km/hr
=
61.6 km/hr.
EXAMPLE 4:
A man covers a certain distance between his house and office on scooter.
Having an average speed of 30 km/hr, he reaches his office 5 min earlier. Find
the distance between his house and office.
Solution: let the distance be x km.
Time
taken to cover x km at 30 km/hr = x/30 hrs.
Time
taken to cover x km at 40 km/hr = x /40 hrs.
Difference
between the time taken = 15 min = ¼ hr.
X/30
– x/40 = ¼
Or
4x – 3x = 30
Or
x
= 30
hence,
the required distance is 30 km.
DIRECT FORMULA:
Thus
, in this case, the required distance
=
30*40/40-30 × 10+5/60
=
30 km
Note: 10 minutes late and 5 minutes
earlier make a difference of 10 + 5 = 15 minutes. As the other unites are in
km/hr, the difference in time should also be changed into hours.
EXAMPLE 5: A man walking with a speed of 5
km/hr reaches his target 5 minutes late. If he walks at a speed of 6 km/hr, he
reaches on time. Find the distance of his target from his house.
Solution: This is similar to Ex. 4. Here
the difference in time is 5 minutes only.
Thus,
required distance = 5*6 / 6-5 * 5/60
=
5 / 2 km
=2.5
km
EXAMPLE 6: A boy goes to school at a speed
of 3 km/hr and returns to the village at a speed of 2 km/hr. If he takes 5 hrs
in all, what is the distance between the village and the school?
Solution: let the required distance be x
km.
Then
time taken during the first journey = x/3 hr.
And
time taken during the second journey = x/2 hr
x/3
+ x/2 = 5
2x+3x
/ 6 = 5
5x
= 30.
X
= 6
Required
distance = 6 km
DIRECT FORMULA:
=
5 × 3*2 / 3+2
=
6 km
EXAMPLE 7: A motor car does a journey in 10
hrs, the first half at 21 km/hr and the second half at 24 km/hr. Find the
distance.
Solution: this question is similar to
Example 6, but we can’t use the direct formla in this case. If we use the above
formula, we get half of the distance. See the detailed method first.
Let
the distance be x km.
Then,
x/2 km is travelled at a speed of 21 km/hr and x/2 km at a speed of 24 km/hr.
Speed
of 24 km/hr.
Then
time taken to travel the whole journey
=
x/2*21 + x/2*24
=
10 hrs.
So,
x = 2*10*21*24 / (21+24)
=
224 km
Direct formula:
Distance
= 2 * time * S1 * S2 / S1 + S2
Where
, s1 = speed during first half and
S2
= speed during second half of journey
Distance
= 2*10*21*24 / 21+24
=
224 km
EXAMPLE 7: A man takes 8 hrs to walk to a
certain place and ride back. However, he could have gained 2 hrs, if he had
covered both ways by riding. How long would he take to walk both ways?
Solution:
walking time + riding time = 8 hrs ........... (1)
2
* riding time = 8 – 2 = 6 hrs ........................................ (2)
Performing
2 * (1) – (2) gives the result
2
* walking time = 2 * 8 – 6 = 10 hrs.
Both
ways walking will take 10 hrs.
DIRECT FORMULA: Both ways walking
=one
way walking and one way riding time + Gain in time
=
8 + 2 = 10 hrs.
To view other quantitative study notes clickhere
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