Chapter 10: Direct and Inverse Proportions

Ans: Total no. Of keys = 7

No of white keys = 10

Their ratio = $\dfrac{10}{7}$

Ans: No of all keyboard = 10+7=17

Ration of black keys to all keys = $\dfrac{7}{17}$

Ans: Black keys in 1 keyboard = 7

Black keys in 14 such keyboards = 14×7=98keys

Ans: This table describes the relation between liters of gas and the distance covered is direct proportional.

The car can cover in 8l of gas = 8×15=120km

Ans: Remaining sugar = $\dfrac{1}{6}$

Used sugar = 1- $\dfrac{1}{6}$ = $\dfrac{5}{6}$

Sugar syrup needed for 1 piece of bread = $\dfrac{1}{3}$

New portion of the ingredients will be =$\dfrac{1}{2}$

New recipe will look like as follows

$\dfrac{1}{2}$ cup quick cooking oats 1 cup bread flour

$\dfrac{1}{6}$ cup sugar syrup$ \dfrac{1}{2}$  cup sugar syrup

$\dfrac{3}{2}$ tablespoon $\dfrac{2}{3}$  yeast cup water

$\dfrac{1}{2}$ tablespoon salt‘

Ans: Ratio of students and teacher = 35:1

This implies that for every 35 students 1 teacher is necessary

Total number of teachers required for 280 students =$\dfrac{280}{35}$ teachers

Ans: 50 miles/hour = 80 km/hour

1 km = $\dfrac{50}{80}$  = $\dfrac{5}{8}$ miles

To cover a distance of 200 km = $\dfrac{5}{8}$ $\times $ 200 = 125 miles

Ans: 60 posters help Anju’s class to raise =Rs 250

1 poster will help= $\dfrac{250}{60}$ = Rs $\dfrac{25}{6}$

By selling 102 posters they collect = $\dfrac{25}{6}$ $\times $ 102 = 17$\times $25= Rs 425

Ans: On selling 1 poster anju’s class make =Rs $\dfrac{25}{6}$

To raise 2000 they need to sell = $\dfrac{25}{6}$ $\times $2000= 480 poster

In Direct proportions, values of two or more variables depend on each other. If one variable increases or decreases, it will equally affect the other quantity. And the opposite happens in Inverse Proportions, If one quantity increases then the other one has to go down and vice-versa. 

In this chapter, students are familiarized with the concept of Direct and Inverse Proportions or relations. The chapter is not that big and includes only two exercises. And it covers 8 marks in the examinations.

The student will get to know the definition of Direct Proportion and conditions needed to be fulfilled to identify if two quantities are in Direct relations.

Let assume x and y are two variable, and they can said to be in Direct proportion, only if they met these certain conditions:

• If x decreases, y decreases.

• If x increases, y increases.

• x/y = K or x*y = C, Where K and C are constants.

• x1/y1 = x2/y2, where y1 is the value of y at x1 , and the same is true for y2.

We, represent x is proportional to y, as such y ∝ x. A real life example of Direct relation can be as if the more fuel put in a car, the more distance the car will cover

The student will get to know the definition of Inverse Proportion and conditions needed to be fulfilled to identify if two quantities are in Inverse relations.

Let assume x and y are two variable, and they can said to be in Inverse Proportion, only if they met these certain conditions:

• If x decreases, y Increases.

• If x increases, y decreases.

• x/y = K or x*y = C, Where K and C are constants.

• x1y1 = x2y2, where y1 is the value of y at x1 , and the same is true for y2.

We, represent x is proportional to y, as such y ∝ 1/x. A real-life example for Inverse Proportion can be that, if the speed of a car increases, the time taken to cover the same distance will decrease.