DAV Class 8 Maths Chapter 6 Value Based Questions
Compound Interest Value Based Questions
1.
Donating blood is a humanitarian act. As per a survey, 16,000 blood donors
are registered with 'Red Cross' in Delhi and this number of donors increases
at the rate of 5% every six months.
(a) How many donors would be there at the end of \(1\dfrac{1}{2}\) years?
(b) Why is it important to donate blood?
(c) What steps would you take to encourage people to donate blood?
Solution
(a) Calculating donors after \(1\dfrac{1}{2}\) years
\[ \begin{aligned} \text{Present donors }(P) &= 16000 \\[6pt] \text{Increase rate per half-year }(R) &= 5\% \\[6pt] n &= 3\ \text{half-years} \end{aligned} \]\[ \begin{aligned} \color{magenta}\textbf{Donors after }1\dfrac{1}{2}\text{ years} &= \color{magenta} P\left(1 + \frac{R}{100}\right)^n \\[10pt] &= 16000\left(1 + \frac{5}{100}\right)^3 \\[10pt] &= 16000\left(\frac{105}{100}\right)^3 \\[10pt] &= 16000\left(\frac{21}{20}\right)^3 \\[10pt] &= \frac{16000 \times 21 \times 21 \times 21}{20 \times 20 \times 20} \\[10pt] &= \frac{16000 \times 9261}{8000} \\[8pt] &= 2 \times 9261 \\[6pt] &= 18522 \end{aligned} \]Answer Donors after \(1\dfrac{1}{2}\) years \(= \color{red}{18{,}522}\)
(b) Blood donation is vital because it saves lives.
(c) To encourage donation, I would spread awareness about eligibility and safety, organize campus or community blood drives with reminders, invite doctors to address myths, and appreciate donors with certificates or social recognition.
2.
A town has a population of 2,50,000. The growth rate of the population of the town is 4% per annum.
(a) What would be the population after three years?
(b) What are the harmful effects of such a rapid increase in the population?
Solution
(a) Calculating population after 3 years
\[ \begin{aligned} \text{Present population }(P) &= 250000 \\[6pt] R &= 4\% \text{ per annum} \\[6pt] n &= 3\ \text{years} \end{aligned} \]\[ \begin{aligned} \color{magenta}\textbf{Population after 3 years} &= \color{magenta} P\left(1 + \frac{R}{100}\right)^n \\[10pt] &= 250000\left(1 + \frac{4}{100}\right)^3 \\[10pt] &= 250000\left(\frac{104}{100}\right)^3 \\[10pt] &= 250000\left(\frac{26}{25}\right)^3 \\[10pt] &= \frac{{{\cancel{250000}^{\cancel{\ 10000}}}^{\cancel{\ 400}}}^{16} \times 26 \times 26 \times 26}{\cancel{25}_1 \times \cancel{25}_1 \times \cancel{25}_1} \\[10pt] &= \frac{250000 \times 17576}{15625} \\[8pt] &= 16 \times 17576 \\[6pt] &= 281216 \end{aligned} \]Answer (a) Population after 3 years \(= \color{red}{2{,}81{,}216}\)
(b) Rapid population rise can strain water, food and housing, increase unemployment, add traffic and pollution, and put pressure on schools and hospitals, reducing overall quality of life.