The following table shows the number of workers and the number of days to finish the construction of water tank in school.

**Inverse
Proportion**

Let us consider the following situation.

**Situation**

The following table shows the number of workers
and the number of days to finish the construction of water tank in school.

In this situation, the two quantities namely number
of workers and the number of days are related to each other. We observe that when
the number of workers increases, the number of days to finish the job decreases.
Consider the number of workers as* x *and
the number of days as* y *then we note that
the product is always the same. That is,

*x* ×*
y *= 2 × 40 = 4 × 20 = 5 × 16 = 10 × 8

Consider each of the value of* x *and the corresponding value of y. Their
products are all equal say *xy* = 80 = k
(k is a constant) and it can be expressed as *xy* = k (k is a constant)

If *y*_{1}
and *y*_{2} are the values of* y *corresponding to the values of *x*_{1} and *x*_{2} of* x *respectively
then *x*_{1} *y*_{1} = *x*_{2} *y*_{2}
(=*k*) *x*_{1}/*y*_{1}
= *x*_{2}/*y*_{2} . We say that* x
*and* y *are in inverse proportion.

** **

**Think**

Think of an example in real life where
two variables are inversely proportional.

**Try these**

**1. Complete the table given below and find the type of proportion**

**2. Read the following examples and group them in two categories**

**Activity**

Form all possible rectangles with
area 36* sq.cm *by completing the following
table.

Observe and answer the following

(i) When length decreases, the breadth __increases__

(ii) When breadth increases, the length __decreases__

(iii) If the length is 8* cm *what will be the breadth? -Discuss.

**Breadth will 4.5 cm**

Extend this activity and try the same
with area 24 and 48 *sq.units*.

** **

__Example 4.5__

60 workers can spin a bale of cotton in 7 days.
In how many days will 42 workers spin it?

**Solution**

Let* x *be
the required number of days. The decrease in number of workers lead to the increase
in number of days. (Therefore, both are in inverse proportion)

For inverse proportion x_{1}y_{1} = x_{2}y_{2}

Hence 60 × 7 = 42 × x

42 ×* x *=
60 × 7

* x* =
60×7 / 42

* x* =
10

In 10 days 42 workers can spin a bale of cotton.

** **

__Example 4.6__

The cost of 1 box of tomato is ₹ 200.
Vendan had money to buy 13 boxes. If the cost of the box is increased to ₹ 260
then how many boxes will he buy with the same amount?

**Solution**

The
cost of one box = ₹ 200

Increased
cost of one box = ₹ 260

Let* x *be the number of boxes bought by Vendan.

As
cost of boxes increases the number of boxes decreases.

This is in inverse proportion. Therefore, *x*_{1}*y*_{1} = *x*_{2}*y*_{2}

13
× 200 =* x *× 260

*x* × 260 = 13
× 200

*x* = [13 × 200]
/ 260

*x* = 10

Therefore, he can buy 10 boxes for the same amount.

Direct and indirect proportion is
very much useful in project scheduling. A project can be any work that is time bound
like building a house, construction of bridges, etc.

Tags : Term 1 Chapter 4 | 7th Maths , 7th Maths : Term 1 Unit 4 : Direct and Inverse Proportion

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7th Maths : Term 1 Unit 4 : Direct and Inverse Proportion : Inverse Proportion | Term 1 Chapter 4 | 7th Maths

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