A man sold Rs 100 shares at $10 %$ discount and invested in $15 %$ rupees fifty shares at Rs 33. Had he sold his shares at $10 %$ premium instead of $10 %$ discount, he would have earned Rs 450 more. Find the number of shares sold by him.
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Solution

Steps: 2 Marks
Formula: 1 Mark
Answer: 1 Mark

Suppose, the man sold $x$ shares.
S.P. of $x$ shares = Rs 90 $x$ (sold at $10 %$ discount)
S.P. of $x$ shares sold at $10 %$ premium = Rs 110 $x$
No. of shares (each of Rs 50) that can be purchased with Rs 90 $x$ = $\frac{90 x}{33}$
Now, income on one Rs 100 share is Rs 15,
$∴$ Income on Rs 50 will be Rs $\frac{15}{2}$
Hence, Annual income = $R s (\frac{15}{2} \times \frac{90 x}{33}) = R s \frac{225 x}{11}$
No. of shares (each of Rs 50) that can be purchased with Rs 110 $x$ = $\frac{110 x}{33}$
Annual income = $R s (\frac{15}{2} \times \frac{110 x}{33}) = R s 25 x$
$25 x - \frac{225 x}{11} = 450 \Rightarrow x = 99$

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A man sold Rs 100 shares at 10% discount and invested in 15% rupees fifty shares at Rs 33. Had he sold his shares at 10% premium instead of 10% discount, he would have earned Rs 450 more. Find the number of shares sold by him. [4 MARKS]

A man sold Rs 100 shares at $10 %$ discount and invested in $15 %$ rupees fifty shares at Rs 33. Had he sold his shares at $10 %$ premium instead of $10 %$ discount, he would have earned Rs 450 more. Find the number of shares sold by him.
[4 MARKS]