DAV Class 8 Maths Chapter 9 Value Based Questions
Linear Equations in One Variable Value Based Questions
1. If a scooterist drives at the rate of 24 km/hr from his home, he reaches his work place 5 minutes late. But if he drives at the rate of 30 km/hr, he reaches his work place 4 minutes early.
(a) Find the distance of his work place from his home.
Solution
\[ \begin{aligned} \text{Let the distance be } &= x \text{ km} \\[6pt] \color{magenta} \textbf{Reaching} & \color{magenta}\textbf{ work late} \\[6pt] \text{Speed} &= 24 \text{ km/hr} \\[6pt] \text{Time} &= \frac{\text{Distance}}{\text{Speed}} \\[6pt] \text{Time} &= \frac{x}{24} \text{ hours} \\ \\ \color{magenta} \textbf{Reaching} & \color{magenta}\textbf{ work early} \\[6pt] \text{Speed} &= 30 \text{ km/hr} \\[6pt] \text{Time} &= \frac{x}{30} \text{ hours} \\[6pt] \textbf{Difference in time } &= \text{late} + \text{early} \\ &= 5 + 4 \\ &= 9 \text{ minutes} \\ \\ \textbf{Convert to hrs }&= \frac{9}{60} \text{ hours} \\[6pt] &= \frac{3}{20} \text{ hours} \\[6pt] \textbf{According to the} & \textbf{ question} \\[6pt] \textbf{Difference in time } &= \frac{3}{20} \\[6pt] \frac{x}{24} - \frac{x}{30} &= \frac{3}{20} \\[6pt] \frac{5x - 4x}{120} &= \frac{3}{20} \\[6pt] \frac{x}{120} &= \frac{3}{20} \\[6pt] x &= \frac{3}{20} \times 120 \\[6pt] \color{green} x &= \color{green} 18 \text{ km} \end{aligned} \]Answer The distance is \( \color{red} 18 \text{ km} \)
(b) Is it advisable to drive at high speed? Give reason
Answer No, it is not advisable to drive at high speed as it increases the risk of accidents.
2. DAV school wants to give 15 prizes to its students on the values of discipline, politeness and punctuality. If the number of prizes for politeness is five-sixth of the number of prizes for discipline and the number of prizes for punctuality is four-fifths that of number of prizes of politeness then—
(a) Find the number of prizes for each value.
Solution
\[ \begin{aligned} \text{Let the no. of prizes for discipline} &= x \\[6pt] \text{No. of prizes for politeness} &= \frac{5x}{6} \\[6pt] \text{No. of prizes for punctuality} & = \frac{4}{5} \times \frac{5x}{6} \implies \frac{2x}{3} \\[6pt] \textbf{According to the} & \textbf{ question} \\[6pt] \text{Total number of prizes} &= 15 \\[6pt] x + \frac{5x}{6} + \frac{2x}{3} &= 15 \\[6pt] \frac{6x + 5x + 4x}{6} &= 15 \\[6pt] \frac{15x}{6} &= 15 \\[6pt] x &= \frac{15 \times 6}{15} \\[6pt] \color{green} x &= \color{green} 6 \\ \\ \text{Prizes for Discipline} &= 6 \\[6pt] \text{Prizes for Politeness} &= \frac{5}{6} \times 6 \implies 5 \\[6pt] \text{Prizes for Punctuality} &= \frac{2}{3} \times 6 \implies 4 \end{aligned} \]Answer Discipline = \( \color{red} 6 \), Politeness = \( \color{red} 5 \), Punctuality = \( \color{red} 4 \)
(b) Apart from the above three values, write one more value for which the prize can be given to students.
Answer Cleanliness, Honesty, Teamwork, etc.