5 Marks Questions

Question 15 Marks

Fill in the following blanks: $\frac{15}{18}=\frac{\square}{6}=\frac{10}{\square}=\frac{\square}{30}$ [Are these equivalent ratios?]

Answer

We can calculate the numbers at the blank places as follows:
$\frac{15}{18}=\frac{5 \times 3}{6 \times 3}=\frac{5}{6}$
$\frac{5}{6}=\frac{5}{6} \times \frac{2}{2}=\frac{10}{12}$
$\frac{5}{6}=\frac{5}{6} \times \frac{5}{5}=\frac{25}{30}$
Hence,
$5, 12$ and $25$ will come in those blanks respectively
Thus,
We can clearly see that,
$\frac{15}{18}=\frac{5}{6}=\frac{10}{12}=\frac{25}{30}$
All these ratios are equivalent.

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Question 25 Marks

See the figure and find the ratio of number of circles to all the figures inside the rectangle.

Answer

Here we have to calculate the ratio of number of circles to all the figures inside the rectangle.
We know that:
Number of circles $= 2$
Total number of figures $= 7$
Therefore required ratio:
$=\frac{\text { Number of circles }}{\text { Total number of figures }}=\frac{2}{7}$
The ratio is $2:7$

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Question 35 Marks

See the figure and find the ratio of number of squares to all the figures inside the rectangle.

Answer

From the given figure:
Number of squares $= 2$
Total number of figures $= 7$
Hence,
Number of squares to the total number of figures
$= \frac{{{\text{Number}}\,{\text{of}}\,{\text{squares}}}}{{{\text{Total number of figures}}}}$
$= \frac{2}{7}$
The required ratio is $2:7.$

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Question 45 Marks

See the figure and find the ratio of number of triangles to the number of circles inside the rectangle.

Answer

From the given figure we can observe that,
Number of triangles $ = 3$
Number of squares $ = 2$
Number of circles $ = 2$
Hence,
Total number of figures $= 3 + 2 + 2 = 7$
Now,
We can calculate the ratio of the number of triangles to the number of circles as follows:
$=\frac{\text { Number of triangles }}{\text { Number of circles }}$ $=\frac{3}{2}$
The ratio is $3:2.$

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Question 55 Marks

Out of $30$ students in a class, $6$ like football, $12$ like cricket and remaining like tennis. Find the ratio of number of students liking cricket to total number of students.

Answer

We are given that
Number of students liking cricket $= 12$
And,
Total number of students $= 30$
Hence,
The Ratio of number of students liking cricket to the Total number of students in the class can be calculated as follows:
$= \frac{{{\text{Number}}\,{\text{of}}\,{\text{students}}\,{\text{liking}}\,{\text{cricket}}}}{{{\text{Total number of students}}}}$
$= \frac{12}{30}$
$=\frac{2}{5}$

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Question 65 Marks

Out of $30$ students in a class, $6$ like football, $12$ like cricket and remaining like tennis. Find the ratio of number of students liking football to number of students liking tennis.

Answer

As per the question, we have:
Total number of students $= 30$
Number of students that like to play football $= 6$
And, Number of students that like to play cricket $= 12$
Now, The number of students that like tennis
$=$ Total number of students $– ($Number of students liking football $+$ Number of students liking cricket$)$
$= 30 – (6 + 12)$
$= 30 – 18$
$= 12$
Hence,
the ratio of the number of students liking football to the number of students liking tennis
$= \frac{{{\text{Number}}\,{\text{of}}\,{\text{students}}\,{\text{liking}}\,{\text{football}}}}{{{\text{Number}}\,{\text{of}}\,{\text{students}}\,{\text{liking}}\,{\text{tennis}}}}$
$= \frac{6}{12}$
$= \frac{1}{2}$

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Question 75 Marks

Mother wants to divide $₹36$ among her daughters Shreya and Bhoomika in the ratio of their ages. If age of Shreya is $15$ years and age of Bhoomika is $12$ years, find how much Shreya and Bhoomika will get$?$

Answer

Total money $= ₹36$
Ratio of the ages of Shreya and Bhoomika
$= 15 : 12 =\frac{15}{12}=\frac{15 \div 3}{12 \div 3}[\therefore H.C.F. (15, 12) = 3]$
$=\frac{5}{4} = .5 : 4$
Sum of the ratio $= 5 + 4 = 9$
$\therefore$ Shreya's share $= ₹ \frac{5}{9} \times36 = ₹20$
and, Bhoomika's share $= ₹\frac {4} {9} \times 36 = ₹16$
Hence, Shreya will get $₹20$ and Bhoomika will get $₹16.$

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Question 85 Marks

There are $20$ girls and $15$ boys in a class. What is the ratio of number of girls to the total number of students in the class?

Answer

The strength of girls $= 20$
The strength of boys $= 15$
Now, Total number of students $=$ Number of girls $+$ Number of boys
$= 20 + 15 = 35$
Therefore, the ratio of the number of girls to the total number of students in the class can be calculated as given below:
$= \frac{\text {Number of girls}}{\text {Total number of students }} = \frac{20}{35} = \frac{4}{7}$
Thus, the ratio of number of girls to the total number of students is: $4 : 7$

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Question 95 Marks

There are $20$ girls and $15$ boys in a class. What is the ratio of a number of girls to the number of boys$?$

Answer

Given that the number of girls $= 20$
and, the number of boys $= 15$
Now,
Total number of students $=$ Number of girls $+$ Number of boys
$= 20 + 15$
$= 35$
Hence, the ratio of number of girls to boys
$= \frac{\text { Number of girls }}{\text { Number of boys }}$
$= \frac{20}{15}$
$= \frac{4}{3}$
Thus the required ratio of girls to boys is $4:3$

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Question 105 Marks

In a college, out of $4320$ students, $2300$ are girls. Find the ratio of number of boys to the total number of students.

Answer

Given that:
Total number of students $= 4320$
Also,
Number of girls $= 2300$
Therefore, number of boys $= 4320 - 2300 = 2020$
So, the required ratio $ = \frac{2020}{4320}$
$= \frac{2 \times 2 \times 5 \times 101}{2 \times 2 \times 5 \times 216}$
$= \frac{101}{216}$
Ratio is $101 : 216$

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