Question

A man invests Rs 12,500 partly in shares of face value Rs 100 each paying $6\%$ at Rs 140 and the remaining in shares paying $5\%$ at Rs 125. If his total income is Rs 520, how much has he invested in each?
[4 MARKS]

Answer 1

Steps: 2 Marks
Amount invested in each share: 1 Mark each

Total investment = Rs 12,500
Let amount invested in first case be Rs $x$
Then amount invested in 2nd case be Rs (12500 - $x$)
Number of shares in 1st case = $\frac{x}{140}$
and number of shares in 2nd case = $\frac{12500-x}{125}$
Total face value in Ist case = $100\times \frac{x}{140}=Rs\frac{5}{7}x$
Total face value in 2nd case = $\frac{100(12500-x)}{125}$
$=Rs\frac{4}{5}(12500-x)$
Total income = Rs 520
$\therefore 6\%of\frac{5}{7}x+5\%of\frac{4}{5}(12500-x)=520$
$\Rightarrow \frac{6}{100}\times \frac{5}{7}x+\frac{5}{100}\times \frac{4}{5}(12500-x)=520$
$\Rightarrow \frac{30x+28(12500-x)}{700}=520$
$\Rightarrow$ 30$x$ + 350000 - 28$x$ = 520 $\times$ 700
$\Rightarrow$ 2$x$ + 350000 = 364000
$\Rightarrow$ 2$x$ = 14000
$x$ = 7000
$\therefore$ Amount invested in first case = Rs 7000
and amount invested in 2nd case = Rs 12500 - Rs 7000
= Rs 5500