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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