The unitary method is a method to solve arithmetic problems based on variation in quantities. In this method we find the value of a unit and then the value of a required number of units.
Ex- If the price of 6 apples is ₹ 30 and you have to buy 10 apples, then find the price of 10 apples.
first you have to find the price of 1 apple, then find the price of 10 apples
∵ Price of 6 apples = ₹ 30
∴ Price of 1 apple = 30 ÷ 6 = ₹ 5
∴ Price of 10 apples = 5 × 10 = ₹ 50
Direct Proportion :-
Direct proportion is the relation between two quantities if on increasing a quantity, then the other quantity also increase, then both quantities are said to be in direct proportion to each other.
For example- If the speed of a car is increase then the distance covered is also increase.
i.e, first quantity ∝ second quantity
Let the first quantity be x and other y, then
Ex- If the price of 9 bananas is ₹ 72, then find out the price of 12 bananas.
Solution:- Price of 9 bananas = 72
By Formula, More bananas, More price so it is direct proportion
Let the price of 12 bananas be ₹ x
Ex– Mohan walks 120 m everyday, how many kilometers will he walk in 5 weeks.
Solution:- 1 day walk = 120 m
Total days = 5 × 7
= 35 days
Total walking distance = 120 × 35
= 4200 m
= 4.2 km ( 1 km = 1000 m )
By formula,
Let the walking distance in 5 weeks or 35 days = x m
More days, more walking distance so it is direct proportion.
⇒ x = 120 × 35
∴ x = 4200 = 4.2 km
Indirect Proportion :-
Indirect proportion is the relation between two quantities if on increasing a quantity, then the other quantity decreases then both quantities are said to be in indirect proportion.
For example- If the speed of car is increase, then time taken is decrease.
Let the first quantity be x and other y, then
Ex- If A travels at a speed of 50 km/h and covers a distance in 8 hours, then how much time will he take to travel the same distance at 80 km/h ?
Solution:- Distance = Speed × time
= 50 × 8
= 400 km
Now to cover the same distance at speed of 80 km/h
By formula, More speed, Less time so it is indirect proportion
x
1 × y
1= x
2 × y
2 = x
3 × y
3 =…….x
n × y
n or, 50 × 8 = 80 × x
Ex- If 30 chains cost ₹ 4650, then how much do 50 chains cost?
Solution:- cost of 30 chains = 4650
By formula, More chains, More cost so it is direct proportion
Let cost of 50 chairs be ₹ x.
Formula- If M1 can do W1 work in D1 days T1 hours per day and M2 person can do W2 work in D2 days T2 hours per day, then
Ex- If 15 men working 12 h per day can reap a field in 24 days, in how many days can 27 men reap the field working 10 h per day ?
Solution:- Let the work completed in x days.
Given, M1 = 15, D1 = 24, T1 = 12, M2 = 27, T2 = 10, D2 = ?
∴ x = 16 days
Ex- 22 men can complete a job in 16 days. In how many days, will 32 men complete that job?
Solution:- Let the work completed in x days.
given, M1 = 22, D1 = 16, M2 = 32, D2 = ?
⇒ 22 × 16 = 32 × x
∴ x = 11 days