Question

Saurav invested 10%, 30% and 40% of his savings in buying shares of 3 different companies A, B and C which declared dividends of 12%, 15% and 16% respectively. If Saurav's total income from dividends is Rs 3,025, find his savings and the amount invested in each company.

Answer 1

Let total savings be x.

Investment in company A = 10 % of x = ${\displaystyle \frac{10}{100}\times x=\frac{x}{10}}$

Investment in company B = 30 % of x = ${\displaystyle \frac{30}{100}\times x=\frac{3x}{10}}$

Investment in company C = 40 % of x = ${\displaystyle \frac{40}{100}\times x=\frac{4x}{10}=\frac{2x}{5}}$

Dividend given by company A = 12 %  of ${\displaystyle \frac{x}{10}}$

${\displaystyle \frac{12\times x}{100\times 10}=0.012 x}$ ........(i)

Dividend given by company B =15 %  of ${\displaystyle \frac{3x}{10}}$

=${\displaystyle \frac{15\times 3x}{100\times 10}=0.045 x}$ ...............(ii)

Dividend given by company C = 16 % of ${\displaystyle \frac{2x}{5}}$

${\displaystyle \frac{16\times 2x}{100\times 5}=0.064 x}$  ..............(iii)

(i) + (ii) +(iii) =Rs 3,025 ........... (given) 

(0.012 + 0.045 + 0.064)x = Rs 3,025 

0.12 l x=Rs 3,025 

x = Rs ${\displaystyle \frac{3025}{0.121}}$ = Rs 25000

Hence, Saurav's savings = Rs 25,000 

Investment in company A = Rs ${\displaystyle \frac{x}{10}}$ = Rs ${\displaystyle \frac{25000}{10}}$ = Rs 2500

Investment in company B = Rs ${\displaystyle \frac{3x}{10}}$ = Rs ${\displaystyle \frac{75000}{10}}$ = Rs 7500

Investment in company C = Rs ${\displaystyle \frac{2x}{5}}$ = Rs ${\displaystyle \frac{50000}{5}}$ = Rs 10000