Question 1

If $x$ and $y$ are in direct proportion, which of the following relations is always true?

Accepted Answer

When two quantities $x$ and $y$ are in direct proportion, their ratio $\frac{x}{y}$ remains constant ($k$). Therefore, $x = ky$, or $\frac{x1}{y1} = \frac{x2}{y2}$.

Question 2

If $x$ and $y$ are in inverse proportion, which of the following is constant?

Accepted Answer

When two quantities $x$ and $y$ are in inverse proportion, their product $xy$ remains constant ($k$). That is, as one increases, the other decreases in such a way that their product is always the same.

Question 3

If 15 pens cost ₹ 75, what is the cost of 1 graph of direct proportion? Find the cost of 10 pens.

Accepted Answer

Let the cost of 10 pens be $x$. Since the number of pens and cost are in direct proportion, $\frac{15}{75} = \frac{10}{x}$. Solving gives $x = \frac{10 	imes 75}{15} = 50$.

Question 4

If 6 workers can build a wall in 12 hours, how many hours will 9 workers take to build the same wall?

Accepted Answer

This is an inverse proportion problem because more workers take less time. Let the time be $x$. $6 	imes 12 = 9 	imes x \implies x = \frac{6 	imes 12}{9} = 8$ hours.

Question 5

A car covers a distance of 160 km in 2 hours. How much distance will it cover in 5 hours at the same speed?

Accepted Answer

Distance and time are in direct proportion. $\frac{160}{2} = \frac{x}{5} \implies x = \frac{160 	imes 5}{2} = 400$ km.

Direct and Inverse Proportions