Direct And Indirect Proportion With Chain Rule Problems Tricks With Examples

In this, we further go through Ratio & Proportion problems which is the Chain rule. Before that let’s see a related concept:

Direct proportion:  It can be defined as a relation where if one quantity x increases then other quantity y increases too. For example, the relation between distance and time. With example, it can be defined as if the distance travelled by a car increases then the required time to reach that distance would also increase.

x/y = k

Indirect proportion:  It can be defined as a relation where one quantity x increases then other quantity y decreases. For example, the relation between speed and time. With example, it can be defined as if the speed of a car increases then the required time to reach the same distance would decrease.

x*y=k

Must Read : Ratio and Proportion Problems Tricks And Shortcuts With Examples

Type of Questions Asked from Chain Rule Problems, Direct & Indirect Proportion

• Question based on the Chain rule

  • Use formula M₁D₁H₁/W₁ = M₂D₂H₂/W₂
  • You will get M₁D₁H₁W₂ = M₂D₂H₂W₁

M = Men Power/Number of things

D = Number of Days

H = Number of Hours

W = Work Done

Q. 3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?M₁ = 3

D₁ = 2

H₁ = 8

M₂ = 4

D₂ = 1

H₂ = x

M₁D₁H₁W₂ = M₂D₂H₂W₁

When W is not given assume it as 1,

3*2*8 =4*1*x

48=4*x

12=x

Alternate or Trick

• First, make a table
• Check the relation whether it is indirect or direct
• Write the given relation in the form of the ratio
  • If it is direct proportion write the ratio as  it is
  • If it is indirect proportion write the ratio in reverse
• Multiply means and extremes [ Check here if you don’t know what are they]

Find whether the relation is direct or indirect b/w given quantities and not given quantities

• In this case, we first see relation b/w pumps and hours. Then, Days and hours
  • If the number of pumps increases to fill a tank, then it would require less time, so it is an indirect proportion, so we write it in reverse ratio
    4:3   [ If it was direct relation then the ratio would be, 3:4]
  • Similarly, b/w Days and hours, suppose, a pump opens each day 8 hours to completely fill the tank in 2 days and now imagine if the same number of pumps need to fill the tank in one day then hours would definitely increase. therefore it is indirect proportion, Again we write it in ratio reversely.

4*1*x = 3*2*8

4x = 48

x=12

• Question based on the direct proportion

  • Make a table
  • And cross multiply it

Q. If a car takes 2 hrs to cover 80km distance. What distance it will cover in 4 hrs?

80km * 4hrs = 2hr * ?

320 km/2= ?

160km

• Question based on the Indirect proportion

  • Make a table
  • And multiply variables opposite to each other horizontally

Q. If a car moves 20 km/h to cover a particular distance in 2 hours. What time it will take to cover the same distance with a speed of 40 km/h?

20 km/h * 2 hrs = 40 km/h * ?

40 /40 = ?

1 hrs