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Question
Mr. Shameem invested `33 1/3%` of his savings in 20% Rs. 50 shares quoted at Rs. 60 and the remainder of the savings in 10% Rs. 100 shares quoted at Rs. 110. If his total income from these investments is Rs. 9,200; find:
- his total savings.
- the number of Rs. 50 shares.
- the number of Rs. 100 shares.
Solution
Let his total savings is Rs. y
1st case:
His saving = `33 1/3%` of `y = Rs. y/3`
The market price of 1 share = Rs. 60
Then shares purchased = `y/(3 xx 60) = y/(180)`
Dividend on 1 share = 20% of Rs. 50 = Rs. 10
Total dividend = `y/180 xx 10 = Rs. y/18`
2nd case:
His saving = `66 2/3%` of `y = Rs. (2y)/3`
Market price of 1 share = Rs. 110
Then shares purchased = `(2y)/(3 xx 110) = y/165`
Dividend on 1 share = 10% of Rs. 100 = Rs. 10
Total dividend = `y/165 xx 10 = Rs. (2y)/33`
According to question
Total income = Rs. 9200
`=> y/18 + (2y)/33 = Rs. 9200`
`=> (23y)/198 = Rs. 9200`
`=> y = (9200 xx 198)/23 = Rs. 79200`
The number of Rs. 50 share = `(79200)/180` = 440
The number of Rs. 100 share = `(79200)/165` = 480
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