In Text Questions Try These (Textbook No.72, 74,75,78) - Chapter 4 Direct and Inverse Proportion Term 1 7th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Text Questions
Try These (Text Book Page No. 72)
Question $1 .$

Find the ratio of the number of circles to number of squares.
Number of circles $=4$;
Number of squares $=6$
Number of circles: Number of squares $=4: 6=2: 3$

Question $2 .$
Find the ratio (i) $555 \mathrm{~g}$ to $5 \mathrm{~kg}$
(ii) $21 \mathrm{~km}$ to $175 \mathrm{~m}$.
Solution:
(i) $1 \mathrm{~kg}=1000 \mathrm{~g}$
$\therefore 5 \mathrm{~kg}=5000 \mathrm{~g}$
$\therefore 555 \mathrm{~g}: 5 \mathrm{~kg}=555 \mathrm{~g}: 5000 \mathrm{~g}=111: 1000$
(ii) $21 \mathrm{~km}$ to $175 \mathrm{~m}$
$1 \mathrm{~km}=1000 \mathrm{~m}$
$21 \mathrm{~km}=21 \times 1000=21,000 \mathrm{~m}$
$\therefore 21 \mathrm{~km}: 175 \mathrm{~m}=21000: 175=120: 1$

Question $3 .$
Find the value of $x$ in the following proportions:
(i) $1108: 88$
(ii) $x: 26: 5: 65$
Solution:
(i) Given $110: \mathrm{x}:: 8: 88$
Product of the means = Product of the extremes
$\mathrm{x} \times 8=110 \times 88$

$x=\frac{110 \times 88}{8}$
$x=1210$

(ii) $x: 26: 5: 65$
Product of the means $=$ Product of the extremes
$\begin{gathered}
26 \times 5=x \times 65 \\
\frac{26 \times 5}{65}=x \\
x=2
\end{gathered}$

Try this (Text Book Page No. 74)
Question $1 .$
The number of chocolates to be distributed to the number of children. Is this statement in direct proportion?
Solution:
Let the number of students be $x$ and the number of chocolates be $y$. As the valve of $x$ increases also correspondingly increases.
ie $\frac{x}{y}=k$
$\therefore x$ and $y$ are in direct proportion.

Try This (Text book Page No. 74)

Question 2.

Observe the following 5 squares of different sides given in the graph sheet.

The measures of the sides are recorded in the table given below. Find the corresponding perimeter and the ratios of each of these with the sides given and complete the table.

From the information so obtained state whether the side of a square is in direct proportion to the perimeter of the square. Solution:
Perimeter of the square $y=4 x$, units where $x$ is the side of a square
If $x=2 ; y=4 \times 2=8 ; \frac{x}{y}=\frac{2}{8}=\frac{1}{4}$
$x=3 ; y=4 \times 3=12 ; \frac{x}{y}=\frac{3}{12}=\frac{1}{4}$
$x=4 ; y=4 \times 4=16 ; \frac{x}{y}=\frac{4}{16}=\frac{1}{4}$
$x=5 ; y=4 \times 5=20 ; \frac{x}{y}=\frac{5}{20}=\frac{1}{4}$
$x=6 ; y=4 \times 6=24 ; \frac{x}{y}=\frac{6}{24}=\frac{1}{4}$

From the above table we find that as $x$ increases $y$ also increased in such a way that $\frac{x}{y}=\frac{1}{4}$, constant. $\therefore$ Side of a square is in direct proportion to the perimeter of the square.

Try this (Text book Page No. 75)
Question $3 .$
When a fixed amount is deposited for a fixed rate of interest, the simple interest changes proportionally with the number of years it is being deposited. Can you find any other examples of such kind.
Solution:
Some other examples of such kind are
(i) Cost of book and number of books
(ii) Distance and time to travel
(iii) Men workers and wages.
 

Exercise $4.2$
Try this (Text book Page No. 78)
Question 1 .
Think of an example in real life where two variable are inversely proportional.
Solution:
Example of inverse proportion are
(i) Men working and the amount of work.
(ii) Speed and time to travel

Try These (Text book Page No. 78)

Question 1.

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

Question 2.

Read the following examples and group them in two categories

Solution: