Answer :
Let's solve each of the questions step-by-step:
Q-4: If the ratio [tex]15:10 :: x:20[/tex], then find the value of [tex]x[/tex].
To find [tex]x[/tex], we use the property of proportions, which states that if [tex]\frac{a}{b} = \frac{c}{d}[/tex], then [tex]a \times d = b \times c[/tex].
For [tex]15:10 :: x:20[/tex]:
[tex]15 \times 20 = 10 \times x[/tex]
[tex]300 = 10x[/tex]
Dividing both sides by 10 gives:
[tex]x = \frac{300}{10} = 30[/tex]
So, the value of [tex]x[/tex] is 30.
Q-5: Which pair of ratios are equal? Why?
a) [tex]\frac{2}{3}[/tex] and [tex]\frac{4}{6}[/tex]
b) [tex]\frac{4}{5}[/tex] and [tex]\frac{12}{20}[/tex]
Let's compare the ratios:
a) [tex]\frac{2}{3}[/tex] and [tex]\frac{4}{6}[/tex]:
Reduce [tex]\frac{4}{6}[/tex] by dividing the numerator and denominator by their greatest common divisor (GCD), which is 2:
[tex]\frac{4}{6} = \frac{4 \div 2}{6 \div 2} = \frac{2}{3}[/tex]
So, these two ratios are equal.
b) [tex]\frac{4}{5}[/tex] and [tex]\frac{12}{20}[/tex]:
Reduce [tex]\frac{12}{20}[/tex] by dividing by their GCD, which is 4:
[tex]\frac{12}{20} = \frac{12 \div 4}{20 \div 4} = \frac{3}{5}[/tex]
These ratios are not equal to [tex]\frac{4}{5}[/tex].
Thus, option a) [tex]\frac{2}{3}[/tex] and [tex]\frac{4}{6}[/tex] are equal.
Q-6: If the ratio [tex]7:36 :: x:15[/tex], then find the value of [tex]x[/tex].
Using the property of proportions:
[tex]7 \times 15 = 36 \times x[/tex]
[tex]105 = 36x[/tex]
Dividing both sides by 36 gives:
[tex]x = \frac{105}{36} \approx 2.9167[/tex]
Rounding to two decimal places, [tex]x \approx 2.92[/tex].
Q-7: The ratio of 6 books to 30 books.
The ratio of 6 books to 30 books can be written as [tex]\frac{6}{30}[/tex].
Simplifying this fraction by dividing the numerator and the denominator by their GCD, which is 6:
[tex]\frac{6}{30} = \frac{6 \div 6}{30 \div 6} = \frac{1}{5}[/tex]
Therefore, the ratio of 6 books to 30 books is [tex]1:5[/tex].
