Page 138 - Maths Skills - 8

136 Maths

INVERSE PROPORTION
In direct proportion between two quantities, say p and q, we have seen that

(i) When one quantity (p) increases the other quantity (q) increases proportionately.
(ii) When one quantity (p) decreases the other quantity (q) decreases proportionately.
Now, let us consider an example given below:
Suppose one person can complete a job in 16 days. Clearly, 2 persons can complete it in 8 days. The number of
days required to complete the same job when worked by 4, 8 and 16 persons are given in a table as under:
Number of persons (p) 1 2 4 8 16

Number of days required (q) 16 8 4 2 1

From the above table, we may notice that the more the number of persons engaged in a job, the less is the number
of days required to complete the same job.

Also, we see that in each case p × q = 16 for each value of p and its corresponding value q.
So, here p and q vary inversely in this example.
Thus, if two quantities p and q vary inversely as each other, then the product pq always remains constant. The
product pq is called the constant of proportion.
Let , pq = K, where K is a positive constant. Fact-o-meter
If p and q , and p and q are in inverse proportion,
1 1 2 2 In inverse proportion,
then, p q = p q = K xa 1
1
1
2 2
p q y
⇒ p 1 = q 2 or xy = constant
2 1
⇒ p : p = q : q
1 2 2 1
Thus, we obtain a rule, that if two quantities p and q vary inversely as each other, then the ratio of any two values
of p is equal to the inverse ratio of the corresponding values of q.

Let’s Attempt

Example 1: A garrison of 400 men had provisions for 90 days. However, a reinforcement of 200 men arrived.
For how many days will the food last now?
Solution: Suppose the food is enough for x days, then
Number of men (p) 400 600 (400 + 200)
Number of days (q) 90 x

Clearly, the more the number of men, the less will be the number of days for which the provisions
will last. Alternative Approach
So, it is a case of inverse proportion. men days

The ratio of the number of men = inverse ratio of the number of days. 400 57
So, 400 : 600 = x : 90 600 x
400 x x 400
⇒ = Here, =
600 90 90 600
⇒ 600 × x = 400 × 90 90 400
or x
400 × 90 36000 600
⇒ x = = = 60
600 600 = 60 days