Direct Proportion

Two quantities a and b are said to be in direct proportion if

  • Increase in a increases the b
  • Decrease in a decreases the b

But the ratio of their respective values must be the same.

  • a and b will be in direct proportion if  \mathrm{\dfrac{a}{b}} = k(k is constant) or a = kb.
  • In such a case if b1, b2 are the values of b corresponding to the values a1, a2 of a respectively then, \mathrm{\dfrac{a_1}{b_2}=\dfrac{a_2}{b_1}}

Symbol of Proportion

When two quantities a and b are in proportion then they are written as a \propto b where \propto represents “is proportion to”.

Methods to solve Direct Proportion Problems

There are two methods to solve the problems related to direct proportion-

1. Tabular Method

As we know that


So, if one ratio is given then we can find the other values also. (The ratio remains the constant in the direct proportion).


The cost of 4-litre milk is 200 Rs. Tabulate the cost of 2, 3, 5, 8 litres of milk of same quality.


Let X litre of milk is of cost Y Rs.


We know that as the litre will increase the cost will also increase and if the litre will decrease then the cost will also decrease.


 \text{a}) \dfrac{X_{1}}{Y_{1}}=\dfrac{X_{2}}{Y_{2}}
 4 Y_2=2 \times 200
 Y_2=\dfrac{2 \times 200}{4}

So the cost of 2 litre milk is Rs.100

 \text{b})\ \dfrac{X_1}{Y_1}=\dfrac{X_3}{Y_3}
 4 Y_3=3 \times 200
 Y_3=\dfrac{3 \times 200}{4}

So the cost of 3 ltr milk is Rs. 150

 \text{c})\ \dfrac{X_1}{Y_1}=\dfrac{X_4}{Y_4}
 4 Y_4=5 \times 200
 Y_4=\dfrac{5 \times 200}{4}

So the cost of 5 ltr milk is Rs. 250

 \text d)\ \dfrac{X_{1}}{Y_{1}}=\dfrac{X_{5}}{Y_{5}}
 4 Y_5=8 \times 200
 Y_5=\dfrac{8 \times 200}{4}

So the cost of 8 litre milk is Rs. 400

2. Unitary Method

If two quantities a and b are in direct proportion then the relation will be

\mathrm{k=\dfrac{a}{b}\ or\ a=k}

We can use this relation in solving the problem.


If a worker gets 2000 Rs. to work for 4 hours then how much time will they work to get 60000 Rs.?



\mathrm{k=\dfrac{No.\ of\ hours}{Salary\ of\ worker}=\dfrac{4}{2000}=\dfrac{1}{500}}


Hence, they have to work for 12 hours to get Rs. 60000

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