DAV Class 8 Maths Chapter 6 Enrichment Question
Compound Interest Enrichment Question
1. A builder employed 4,000 workers to work on a residential project. At the end of the first year, 10% workers were removed, at the end of the second year, 5% of those working at that time were retrenched. However, to complete the project in time, the number of workers was increased by 15% at the end of the third year. How many workers were working during the fourth year?
Solution
\[ \begin{aligned} \text{Initial workers }(P) &= 4000 \\[6pt] \text{Workers removed } (a) &= 10 \% \\[6pt] \text{Workers removed } (b) &= 5 \% \\[6pt] \text{Workers added } (c) &= 15 \% \\[6pt] \end{aligned} \] \[ \begin{aligned} \color{magenta}\textbf{Workers during the fourth year} &= \color{magenta} P\left(1 - \frac{a}{100}\right) \left(1 - \frac{b}{100}\right)\left(1 + \frac{c}{100}\right) \\[10pt]\end{aligned} \]\[ \begin{aligned} & = 4000 \left(1 - \frac{10}{100}\right) \left(1 - \frac{5}{100}\right)\left(1 + \frac{15}{100}\right) \\[10pt] & = 4000 \left(1 - \frac{1}{10}\right) \left(1 - \frac{1}{20}\right)\left(1 + \frac{3}{20}\right) \\[10pt] & = 4000 \left(\frac{10 - 1}{10}\right) \left(\frac{20 - 1}{20}\right)\left(\frac{20 + 3}{20}\right) \\[10pt] & = 4000 \left(\frac{9}{10}\right) \left(\frac{19}{20}\right)\left(\frac{23}{20}\right) \\[10pt] &= 9 \times 19 \times 23 \\ &= 3933 \end{aligned} \]Answer Workers during the fourth year \(= \color{red}{3{,}933}\)