Question

Mr. Shameen invested $33\dfrac{1}{3}%$ of his savings in $20%$ Rs 50 shares quoted at Rs 60 and the remainder of his savings in $10%$ Rs 100 shares quoted at Rs 110. If his total income from these investments is Rs 9200. Find his total savings.

Answer 1

Hint: We will start by assuming that Mr. Shameen had y Rs in his savings. Now we are given that he invested $33\dfrac{1}{3}%$ of y in a share quoted at 60 Rs. Hence we will calculate the number of shares brought by the unitary method. Now we are given that he got a dividend of 20 percent of Rs 50 per share. Hence we can calculate the dividend per share and hence Dividend received by Mr. Shameen. Now we are given that the rest of savings are invested in other shares. Hence we can say that $\left( 100-33\dfrac{1}{3} \right)%$ of y was invested in other shares. Hence we will again find out the number of shares brought. Now dividend received on this share is 10 percent of 100. Hence we get the dividend received per share and thus the total Dividend received by Mr. Shameen.
Now the total income through this is the sum of Dividend received in both cases. Hence we get a linear equation in y which can easily be solved to find the value of y.

Complete step by step answer:
Now let us assume that Mr. Shameen had a total saving of y Rs.
It is given that he invested $33\dfrac{1}{3}%$ of his savings in a share.
Now we know that $33\dfrac{1}{3}=\dfrac{33\times 3+1}{3}=\dfrac{99+1}{3}=\dfrac{100}{3}$
Hence, we have $33\dfrac{1}{3}%\times y=\dfrac{100}{3}%\times y=\dfrac{100}{3\times 100}\times y=\dfrac{y}{3}Rs$
Hence we know he invested $\dfrac{y}{3}Rs$
Now the shares were quoted at 60 Rs. Hence for 60 Rs he can by 1 share.
Hence the number of shares that can be bought per rupee is $\dfrac{1}{60}$
Hence the number of shares Mr. Shameen bought in $\dfrac{y}{3}Rs$is \[\dfrac{y}{3\times 60}=\dfrac{y}{180}\]
Now it is given that dividend on 1 share is 20 percent of Rs 50, hence
 $\dfrac{20}{100}\times 50=10Rs$
Hence, dividend on 1 share is 10 Rs.
Now the dividend on $\dfrac{y}{180}$ shares will be $\dfrac{y}{180}\times 10=\dfrac{y}{18}$
Hence the profit income through this share is $\dfrac{y}{18}Rs....................\left( 1 \right)$
Now we are given that he invested rest of his savings in other shares.
Since the first investment was $\dfrac{100}{3}%$ the remaining savings will be $100-\dfrac{100}{3}=\dfrac{300-100}{3}=\dfrac{200}{3}%$
Now $\dfrac{200}{3}%$ of y is \[\dfrac{200}{3\times 100}\times y=\dfrac{2y}{3}\]
We are given that the price of this share is 110 Rs.
This means the price of one share is 110 Rs.
Hence the number of shares that can be brought in 1 Rs is $\dfrac{1}{110}$
Hence, Mr. Shameen brought $\dfrac{1}{110}\times \dfrac{2y}{3}$ shares in $\dfrac{2y}{3}Rs$
Now we are given that dividend of share is $10%$ of Rs 100
Dividend for 1 share $=\dfrac{10}{100}\times 100=10Rs$
Hence total dividend is $\dfrac{1}{110}\times \dfrac{2y}{3}\times 10=\dfrac{2y}{33}$
Hence earnings through this share is $\dfrac{20y}{3}Rs....................\left( 2 \right)$
Now from equation (1) and (2) we get
The total earnings is $\dfrac{2y}{33}+\dfrac{y}{18}$
Taking LCM we get total earning $=\dfrac{12y}{198}+\dfrac{11y}{198}=\dfrac{23y}{198}$
Now since the total earning is given to be 9200 Rs we get
$\begin{align}
  & \dfrac{23y}{198}=9200 \\
 & \Rightarrow y=\dfrac{9200\times 198}{23} \\
 & \Rightarrow y=400\times 198 \\
 & \Rightarrow y=79200 \\
\end{align}$
Hence we get the total savings of Mr. Shameen is 79200 Rs.


Note:
 Now note that percentage is nothing but a fraction with denominator 100. Hence whenever there is mentioned $x%$ it actually means $\dfrac{x}{100}$ . Also, note that the dividend that we get is not the total Dividend but the dividend obtained through each share. Hence we multiply it with the number of shares brought to calculate the total Dividend. With this also remember we use the total number of shares brought and not the price at which it is brought while calculating dividend. For example, If we buy shares worth Rs 500 priced at 100 Rs per share and a dividend is announced as 5 Rs then the total dividend amount is $5\times 5=25$ and not $5\times 500$ as we just brought $\dfrac{500}{100}=5$ shares.