Direct proportion worksheet with answer

Some important Points : 

  • In the direct proportion, if one quatity increases, the other also increases, and If one decreases, the other also decreases 
  • We write Quantities as \frac{x_{1}}{y_{1}} =\frac{x_{2}}{y_{2}}

Q.1 If 192 bananas cost 320 Rs then find how many bananas can be bought for 200 Rs.

Q.2 Rita covers a distance of 165 km in 5\frac{1}{2} hours by car. Assuming, the speed of the car to be constant, how much time will she take to cover a distance of 225 km?

Q.3 If 280 tennis balls cost 1960 Rs . Find the cost of 4 dozen balls 

Q.4 12 books weigh 1.6 kg . What is the weight of 27 such books 

Solution: 

Problem: 01

If 192 bananas cost 320 Rs then find how many bananas can be bought for 200 Rs.

Solution:

Let the required no number of bananas be x 

No. of Bananas (x)            192                         x
Cost of bananas (in Rs ) (y)            320                         200

We know, in direct proportion 

\frac{x}{y}=k   where k is any fixed constant 

Thus ,    \frac{192}{320}=\frac{x}{200}

x=\frac{192×200}{320}=120 

So, Price for 120 bananas be 200 Rs 

Problem : 02 

Rita covers a distance of 165 km in 5\frac{1}{2} hours by car. Assuming, the speed of the car to be constant, how much time will she take to cover a distance of 225 km?

Solution: 

Let the time taken by Rita to cover the distance of 225 km be x 

Distance covered by Rita (in Km)              165                      225 
Time  taken (in hrs )              5\frac{1}{2}                     x

We Know,

\frac{x}{y}=k   where k is any fixed constant 

Thus ,  \frac{165}{5\frac{1}{2}}=\frac{225}{x}

 x=\frac{225×11}{165×2}= \frac{15}{2}

So, Rita will cover distance of 225 km in \frac{15}{2}

Problem : 03 

If 280 tennis balls cost 1960 Rs. Find the cost of 4 dozen balls 

Solution:

Let the cost for 4 dozen balls(48 balls ) be x 

No. of the tennis balls                     280                         48 
Cost of tennis balls (in Rs)                     1960                            x 

We know,

\frac{280}{1960}=\frac{48}{x}

x=\frac{1960×48}{280}

x= 336 

So, the Price for 48 balls or 4 dozen balls be 336 Rs 

Problem: 04 

12 books weigh 1.6 kg . What is the weight of 27 such books 

Solution: 

Let the weight of 27 books is x kg

No. of books                     12                          27 
Weight of books (in kg)                    1.6                           x 

\frac{12}{1.6}=\frac{27}{x}

x=\frac{1.6×27}{12}=3.6

So,Weight of 27 books is 3.6 kg 

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