Q1 of 7 Page 66

Complete the following table showing an instance of inverse proportion. The table shows the number of workers carrying out a task and the number of days they take to do it.

Let the missing values be x, y, z as shown



Let ‘a’ be some value in number of workers and ‘b’ be some value in days


Given a ∝ ⇒ a = k × ⇒ ab = k


When number of workers = 30 i.e. a = 30


days require = 4 i.e. b = 4


using k = ab


⇒ k = 30 × 4


∴ k = 120


As by given it is inverse proportion


⇒ 8x = 10y = 24z = 120


Consider 8x = 120


⇒ x = = 15


∴ x = 15


Consider 10y = 120


⇒ y = = 12


∴ y = 12


Consider 24z = 120


⇒ z = = 5


∴ z = 5


The table becomes



More from this chapter

All 7 →
3

There is direct variation between the sale of books and the commission received for the sale. The table below gives the values of some sales and some commissions. Write the remaining values and complete the table.

 1

In each example, find the constant of proportionality and write the equation of variation.

(1) The quantity y varies directly as x. When the value of y is 20, the value of x is 4.


(2) p α q. When p is 12, the value of q is 18.


(3) c α d. When c = 28, d = 21.


(4) m α n. When m = 7.5, n = 10.

 1

In each example, find the constant of proportionality and write the equation of variation.

(1) When y = 15, x = 14


(2) When w = 24, z = 2.5


(3) When t = 5.5, s = 4.4

2

Sixty crates, each of which can hold 36 mangoes, are required to pack a certain number of mangoes. How many crates, each of which can hold 48 mangoes, will be required for the same number of mangoes? What kind of proportion is there between the number of crates and the number of mangoes in each crate?