Exercise 2.1 - Chapter 2 Percentage and Simple Interest Term 3 7th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Ex 2.1
Question 1.
In each of the following grid, find the numbers of coloured squares and express it as a fraction, decimal and percentage.

Solution:
Total number of squares $=100$
$\therefore$ Fraction : $\frac{58}{100}$
Decimal : $0.58$
Percentage : $58 \%$
(ii) Number of coloured square $=53$
Total number of squares $=100$
$\therefore$ Fraction : $\frac{53}{100}$
Decimal : $0.53$
Percentage : $53 \%$
(iii) Number of coloured square $=25$
Total number of squares $=50$
$\therefore$ Fraction : $\frac{25}{\text { 6i丆 }}$
Decimal : $\frac{25}{50} \times \frac{2}{2}$
$\begin{aligned}
&=\frac{50}{100} \\
&=0.50
\end{aligned}$
Percentage : $\frac{25}{50} \times \frac{100}{100}$
$=\frac{25}{50} \times 100 \%=50 \%$

(iv) Number of coloured square $=17$
Total number of squares $=25$
$\therefore$ Fraction : $\frac{17}{25}$
Decimal : $\frac{17}{25} \times \frac{4}{4}$
$=\frac{68}{100}=0.68$
Percentage : $\frac{17}{25} \times \frac{100}{100}$
$=\frac{17}{25} \times 100 \%$
$=68 \%$
(v) Number of coloured square $=15$
Total number of squares $=30$
$\therefore$ Fraction : $\frac{15}{30}$
Decimal : $\frac{15}{30}$
$\begin{aligned}
&=\frac{1}{2} \times \frac{50}{50} \\
&=\frac{50}{100}=0.50 \\
&\text { Percentage : } \frac{15}{30} \\
&=\frac{15}{30} \times \frac{100}{100} \\
&=\frac{15}{30} \times 100 \% \\
&=50 \%
\end{aligned}$

Question $2 .$
A picture of chess board is given.
(i) Find the percentage of the white coloured squares
(ii) Find the percentage of gray coloured squares
(iii) Find the percentage of the squares that have the pieces and
(iv) The squares that do not have the pieces.

Sulution.
(i) Total number of squares in the chess board $=64$
Number of white coloured squares $=32$
Percentage $=\frac{32}{62} \times \frac{100}{100}$
$=\frac{32}{64} \times 100 \%$
$=50 \%$
(ii) Grey coloured squares $=64$
$P$ ercentage $=\frac{32}{64} \times \frac{100}{100}$=50 \%$

Question $3 .$
A picture of dart board is given. Find the percentage of white coloured portion and black coloured portion.

Solution:
Total sector $=20$
White coloured sector $=10$
Black coloured sector $=10$
Percentage of white : $\frac{10}{20} \times \frac{100}{100}$
Decimal : $\frac{10}{20} \times 100 \%$
= $50 \%$
Percentage of black colour $: \frac{10}{20} \times \frac{100}{100}$
Decimal : $\frac{10}{20} \times 100 \%$
$=50 \%$

Question $4 .$
Write each of the following fraction as percentage.
(i) $\frac{30}{50}$
(ii) $\frac{81}{30}$
(iii) $\frac{42}{50}$
(iv) $2 \frac{1}{4}$
(v) $1 \frac{3}{5}$
Solution:
(i) $\frac{36}{30}$
$\begin{aligned}
&\text { (i) } \frac{30}{30} \\
&=\frac{36}{50} \times \frac{100}{100} \\
&=\frac{36}{50} \times 100 \% \\
&=72 \%
\end{aligned}$
(ii) $\frac{81}{30}$
(iii) $\frac{42}{56}$ $=\frac{42}{56} \times \frac{100}{100}$ $=\frac{42}{56} \times 100 \%$ $=\frac{21}{28} \times 100 \%$ $=75 \%$ (iv) $2 \frac{1}{4}$
$\begin{aligned}
&=\frac{81}{30} \times \frac{100}{100} \\
&=\frac{81}{30} \times 100 \% \\
&=270 \%
\end{aligned}$
$\begin{aligned}
&=\frac{9}{4} \\
&=\frac{9}{4} \times \frac{100}{100} \\
&=\frac{9}{4} \times 100 \\
&=225 \% \\
&\text { (v) } 1 \frac{3}{5}
\end{aligned}$
$\begin{aligned}
&\text { (v) } 1 \frac{3}{5} \\
&=\frac{8}{5} \\
&=\frac{8}{5} \times \frac{100}{100} \\
&=\frac{8}{5} \times 100 \% \\
&=160 \%
\end{aligned}$

Question $5 .$
Anbu scored 436 marks out of 500 in his exams. What was the percentage he scored?
Answer:
Total marks $=500$
Anbu's Score $=436$
Percentage $=\frac{436}{500} \times \frac{100}{100}$
$=87.2 \%$ Anbu"s Score $=87.2 \%$

Question $6 .$
Write each of the following percentage as fraction,
(i) $21 \%$
(ii) $93.1 \%$
(iii) $151 \%$
(iv) $65 \%$
(v) $0.64 \%$
Solution:
(i) $21 \%$
= $\frac{21}{100}$
(ii) $93.1 \%$
$\begin{aligned}
&=\frac{90.1}{100} \\
&=\frac{93.1 \times 10}{100 \times 10} \\
&=\frac{931}{1000}
\end{aligned}$

$\begin{aligned}
&\text { (iii) } 151 \% \\
&=\frac{151}{100}
\end{aligned}$
$\begin{aligned}
&\text { (iv) } 65 \% \\
&=\frac{65}{100} \\
&=\frac{13}{20}
\end{aligned}$
(v) $0.64 \%$
$\begin{aligned}
&=\frac{0.64}{100} \\
&=\frac{0.64 \times 100}{100 \times 100} \\
&=\frac{64}{10000} \\
&=\frac{4}{625}
\end{aligned}$

Question $7 .$
Iniyan bought 5 dozen eggs. Out of that 5 dozen eggs, 10 eggs are rotten. Express the number of good eggs as percentage.
Solution:
1 dozen eggs $=12$
5 dozen $=5 \times 12$
Total eggs $=60 \mathrm{eggs}$
Rotten eggs $=10 \mathrm{Good}$
eggs $=60-10=50$
Fraction of good eggs $=\frac{50}{60}$
Percentage of good eggs $=\frac{50}{60} \times \frac{109}{100}$
$=\frac{60}{60} \times 100 \%$
$\begin{aligned}
&=\frac{5}{6} \times 100 \% \\
&=83.33 \%
\end{aligned}$
Percentage of good eggs $=83.33 \%$

Question $8 .$
In an election, Candidate X secured $48 \%$ of votes. What fraction will represent his votes?
Solution:
Percentage of votes $x$ secured $=48 \%=\frac{48}{100}$
Fraction of votes $x$ secured $=\frac{12}{25}$
 

Question $9 .$
Ranjith total income was $₹ 7,500$. He saved $25 \%$ of his total income. Find the amount saved by him. Solution:
Total income of Ranjith $=₹ 7500$
His savings $=25 \%$ of 7500
$=\frac{25}{100}$ of 7500
$=\frac{25}{100} \times 7500$
$=₹ 1,875$
$\therefore$ Amount saved by Ranjith $=₹ 1,875$
 

Objective Type Questions
Question 1.
Thendral saved one fourth of her salary. Her savings percentage is
(i) $\frac{3}{4}$
(ii) $\frac{1}{4} \%$
(iii) $25 \%$
(iv) $1 \%$
Hint: $\frac{1}{4} \times \frac{100}{100}$
$\begin{aligned}
&=\frac{1}{4} \times 100 \% \\
&=25 \%
\end{aligned}$
Answer:
(iii) $25 \%$

Question $2 .$
Kavin scored 15 out of 25 in a test. The percentage of his marks is
(i) $60 \%$
(ii) $15 \%$
(iii) $25 \%$
(iv) $15 / 25$
Hint: $\frac{15}{25} \times \frac{100}{100}$
$\begin{aligned}
&=\frac{15}{25} \times 100 \% \\
&=60 \%
\end{aligned}$
Answer:
(i) $60 \%$

Question $3 .$
$0.07 \%$ is
(i) $\frac{7}{10}$
(ii) $\frac{7}{100}$
(iii) $\frac{7}{1000}$
(iv) $\frac{7}{10,000}$
Hint. $0.07 \%$
$=0.07 \%$
$=\frac{0.07}{100}$
$=\frac{7}{\frac{10}{1001}}$
$=\frac{7}{100 \times 100}$
$=\frac{7}{10,000}$
Answer:
(iv) $\frac{7}{10,000}$