Question

A person invested $20\%,30\%$ and $25\%$ of his savings in buying shares of three different companies X, Y and Z which declared dividends of $10\%,12\%$ and $15\%$ respectively. If the total income on account of dividends be Rs 2,337.50, find his savings and the amount which he invested in buying shares of each company.
[4 MARKS]

Answer 1

Savings: 1 Mark
Amount invested in each company: 1 Mark each

Let total savings = Rs 100
$\therefore$ Investment in company X = $20\%$ of 100 = Rs 20
Investment in company Y = $30\%$ of 100 = Rs 30
Investment in company X = $25\%$ of 100 = Rs 25
Now, Income from company X = Rs $(\frac{10}{100}\times 20)$=Rs 2
Income from company Y = Rs $(\frac{12}{100}\times 30)$ = Rs 3.60
Similarly, income from company Z = Rs $(\frac{15}{100}\times 25)$=Rs 3.75
Total income = Rs 2 + Rs 3.60 + Rs 3.75 = Rs 9.35
Now, if income is Rs 9.35, then savings = Rs 100
If income is Rs 2,337.50, then savings = Rs $\left(\frac{100\times 2337.50}{9.35}\right)$ = Rs 25,000
$\therefore$ Amount invested in company X = $20\%$ of savings = Rs $\frac{20}{100}\times 25000$
= Rs 5000
Amount invested in company Y = $30\%$ of savings = Rs $\frac{30}{100}\times 25000$ = Rs 7500
Amount invested in company Z = $25\%$ of savings = Rs $\frac{25}{100}\times 25000$ = Rs 6250
Thus, amount invested in companies, X, Y and Z respectively are Rs 5,000, Rs 7,500 and Rs 6,250.