Ratio is not an absolute concept it is relative.
If A : B : C have
money in the ratio 2 : 3 : 4 they could have $2, $3, $4 respectively or
$4, $6, $8 etc...
Question:
a : b = 2 : 7
b : c = 14 : 17
Find a : b : c
Soln: LCM of 7 and 14 = 14
2 : 7 = 4 : 14 Therefore, a : b : c = 4 : 14 : 17
Variation
Variable a one quantity
is dependent on another. A α B means if B ↑ (increases),
A also ↑.
1
A α --- means if
C ↑ A ↓.
C
B
B
Now if A α --- then A =
K ---- (K is Proportionality
constant)
C
C
K would remain constant irrespective of
values of A, B and C.
Work Related Problems
Man-hour: If a person works
10 hrs a day and completes the job in 10 days, job requires 100 man-hours.
If this person works only 5hrs/day he would complete the job in 20
days.
Since 10 × 10 = 5 × 20
8 people working 6 hrs a
day complete the job in 2 days. (96 man-hrs) If 24 people work 4 hrs a day
then they would complete the job in 1 day.
Since 8 × 6 × 2 = 24 × 4× 1
Examples
The first pipe fills the
vessel in 2 mins. There is a leak at the bottom, which can empty the
complete vessel in 3 mins. If vessel is empty and you open the pipe when
will it get full?
Soln: The empty vessel would
be full only if the rate of inflow > the rate of outflow Let the empty
vessel get full in x minutes
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