WORD PROBLEMS ON DIRECT AND INVERSE PROPORTION

Problem 1 :

Suppose 6 kg of salt contains 6 × 10⁷ crystals. How many crystals are there is i) 7 kg of salt   ii) 3.5 kg of salt ?

Solution :

Given, 6 kg of salt contains 6 × 10⁷ crystals.

Then, 1 kg of salt contains 1 × 10⁷ crystals

i) 7 kg of salt  

7 kg of salt contains 7 × 10⁷ crystals

ii) 3.5 kg of salt

3.5 kg of salt contains 3.5 × 10⁷ crystals

Problem 2 :

A machine in a Pepsi factory fills 680 bottles in 5 hrs. How many bottles will it fill in 3 hrs?

Solution :

680 bottles  -----> 5 hrs

x ------> 3 hrs

In less hours, less number of bottles can be filled.

680 ⋅ 3 = x ⋅ 5

x = 680(3) / 5

x = 408 bottles

Problem 3 :

Bacteria enlarged 60000 times attain a length of 3 cm. what is the length of bacteria if it is enlarged 10000 times only.

Solution :

Number of times enlarged        length(cm)

60000                                  3

10000                                  x

60000 ⋅ x = 3 ⋅ 10000

x = 30000/60000

= 0.5 cm

So, length of bacteria is 0.5 cm.

Problem 4 :

A bus travels 40 kms in 30 minutes. If the speed of the bus remains same, how far can it travel in 3 hrs?

Solution :

3 hrs = 180 mins

If number of minutes increases then distance covered will also increase. 

It comes under direct proportion.

40 ⋅ 180 = x ⋅ 30

x = (40 ⋅ 180) / 30

x = 240 km

So, the bus travels 240 km in 3 hours.

Problem 5 :

A contractor estimates that 5 persons could plumb Ravi’s house in 8 days. If he uses 6 persons instead of 5, how long should they take to complete the job.

Solution :

Let x be the number of days taken to complete the job.

If the number persons increases, then number number of days will reduce.

It comes under inverse proportion.

5 ⋅ 8 = 6 ⋅ x

x = 40/6

x = 6   2/3 days

Problem 6 :

If a box of pens is given to 25 children, they will get 2 pens each. How many would each get, if the number of children is reduced by 10?

Solution :

If each person gets 2 pens, then 25 children will get

= 25(2)

= 50 pens

Number of children is reduced, then number of pens got by each children will increase.

10 children each will get = 50/10

= 5 pens

Problem 7 :

A batch of tablets were packed in 10 boxes with 6 tablets in each box. If the same batch is packed using 12 tablets in each box. How many boxes would be needed?

Solution :

10 ⋅ 6 = x ⋅12

x = 60/12

x = 5

x = 5 boxes

So, 5 boxes are needed.

Problem 8 :

In a toy company, it requires 36 machines to produce a car toys in 54 days. How many machines would be required to produce the same number of car toys in 81 days?

Solution :

If number of days increases, then number of machines will decrease.

It comes under inverse proportion.

36 × 54 = x × 81

1944 = 81x

x = 1944/81

x = 24 machines

So, 24 machines would be required.

Problem 9 :

Two persons could fit the AC unit a house in 2 days one person fell ill before the work started, how long would the job take now?

Solution :

If number of persons decreases, then number of days taken will increase.

It comes 

2 × 2 = 1 × x

x = 4 days

So, one person will complete the job in 4 days.

Problem 10 :

In a college 7 period a day each of 45 minutes duration. How long each period be, if the school has 9 periods a day assuming the number of hours to be the same?

Solution :

It comes under inverse proportion.

7 × 45 = 9 × x

315 = 9x

x = 315/9

x = 35 min

So, duration of every period is 35 min.

Problem 11 :

There are 200 students in primary school. They need 50 liters of drinking eater/day. If 50 of them are reduced how many liters of water needed per day?

Solution :

It comes under inverse proportion.

200 × 50 = 150 × x

10000 = 150x

x = 10000/150

x = 66.6 litres

So, 66.6 liters of water is required per day.