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Question
Akanksha invested 15%, 25% and 35% of her savings in buying shares of 'Infosys', 'Wipro' and 'Reliance' which declared dividends of 16%, 18% and 20% respectively. If her total income from dividends is Rs 52,125, find her savings and the amount invested in each company.
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Solution
Let total savings be x.
Investment in ' Infosys' = 15 % of x = `15/100 xx x = (3 x)/20`
Investment in 'Wipro' = 25 % of x = `25/100 xx x = (x)/4`
Investment in 'Reliance' = 35 % of x = `35/100 xx x = (7 x)/20`
Dividend given by 'Infosys' = 16 % of `(3 x)/20`
`= (16 xx 3 x)/(100 xx 20) = 0.024 x` ...........(i)
Dividend given by 'Wipro' = 18 % of `(x)/4`
`= (18 xx x)/(100 xx 4) = 0.045 x` ..........(ii)
Dividend given by 'Reliance' = 20 % of `(7 x)/20`
`= (20 xx 7 x)/(100 xx20) = 0.07 x` ...............(iii)
(i) + (ii) + (iii) = Rs 52, 125 ........... (given)
(0.024 + 0.045 + 0.07 )x = Rs 52, 125
0.139 x=Rs 52, 125
x = Rs `52125/0.139` = Rs 375000
Hence, Akanksha's savings = Rs 3,75,000
Investment in 'Infosys' = Rs `(3 x)/20` = Rs `(3 xx 375000)/20` = Rs 56250
Investment in 'Wipro' = Rs `x/4` = Rs `375000/4` = Rs 93750
Investment in 'Reliance' = Rs `(7 x)/20` = Rs `(7 xx 375000)/20` = Rs 131250
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