WORD PROBLEMS ON DIRECT PROPORTION

Direct proportion is a situation where an increases in one quantity causes a corresponding increases in the other quantity, 

(or)

Direct proportion is a situation where an decreases in one quantity causes a corresponding decreases in the other quantity.

Problem 1 :

A dozen bananas costs $20. What is the price of 48 bananas ?

Solution :

Let ‘x’ be the price of 48 bananas.

As number of banana increases, the price of banana will also increase. 

It comes under direct proportion.

Doing cross multiplication.

12  x  = 48  20

x = (48  20)/12

x = 960/12

x = $80

Therefore, the price of 48 bananas is $80.

Problem 2 :

A group of 21 students paid $840 as the entry fee for a magic show. How many students entered the magic show if the total amount paid was $1,680 ?

Solution :

Let ‘x’ be the number of students entered the magic show.

As number of student increases, the entry fees will also increase. It comes under direct proportion.

Doing cross multiplication.

21  1680  =  x  840

35280 = x  840

35250/840 = x

x = 42

Therefore, 42 students entered the magic show. 

Problem 3 :

A birthday party is arranged in third floor of a hotel. 120 people take 8 trips in a lift to go to the party hall. If 12 trips were made how many people would have attended the party ?

Solution :

Let the number of people have attended the party be ‘x’.

As number of trips increases, number of people also increases.

It comes under direct proportion.

Doing cross multiplication.

120  12 = 8  x

1440 = 8  x

1440/8 = x

x = 180

Therefore, 180 people attended the party in 12 trips.

Problem 4 :

The shadow of a pole with the height of 8 m is 6 m. if the shadow of another pole measured at the same time is 30 m, find the height of the pole ?

Solution :

Let ‘x’ be the required height of the pole.

As length of shadow increases, height of the pole also increases.

It comes under direct proportion.

Doing cross multiplication.

 30 = 6  x

240 = 6  x

240/6 = x

40 m = x

Therefore, the height of the pole is 40 m.

Problem 5 :

A postman can sort out 738 letters in 6 hours. How many letters can be sorted in 9 hours ?

Solution :

 Let ‘x’ be the required number of letters.

As required time to sort in hours is increases, so, the number of letters is also increases.

It comes under direct proportion.

Doing cross multiplication.

738  9 = 6  x

6642 = 6  x

6642/6 = x

1107 = x

Therefore,  1107  letters can be sorted in 9 hours.

Problem 6 :

If half a meter of cloth costs $15. Find the cost of 8 1/3 meters of the same cloth.

Solution :

Let ‘x’ be the cost of 8  1/3 m of the same cloth.

Length of cloth is increases. So, cost of cloth is also increases.  

It comes under direct proportion

Doing cross multiplication.

15  (25/3) = x  1/2

125 = x  1/2

125 x 2 = x

x = $250

Therefore, the cost of 8 1/3 m of cloth is $ 250.

Problem 7 :

The weight of 72 books is 9 kg. What is the weight of 40 such books ?

Solution :

Weight of 72 books = 9 kg

72 books  ---->  9 kg

40 books ----> x kg

Since the number of books increases, the weight of books will also increase. It comes under direct proportion.

Doing cross multiplication, we get

72x = 9(40)

x  =  9(40)/72

x = 5 kg

Weight of 40 books is 5 kg.

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