Question

Mrs. Kulkarni invests Rs. 1,31,040 in buying Rs. 100 shares at a discount of 9%. She sells shares worth Rs. 72,000 at a premium of 10% and the rest at a discount of 5%. Find her total gain or loss in the whole?

Answer 1

Hint: We start solving the problem by finding the cost incurred for buying 1 share to Mrs. Kulkarni. We use this cost to find the total number of shares bought by Mrs. Kulkarni. We then find the total number of shares worth Rs. 72,000 and find the price at which they sold. We then find the number of shares remaining and find the price at which they were sold. We then find the total selling price that all the shares were sold. We then subtract cost from this selling price to get the required value of gain or loss.

Complete step-by-step answer:
According to the problem, we are given that Mrs. Kulkarni invests Rs. 1,31,040 in buying Rs. 100 shares at a discount of 9%. We need to find the total gain or loss of her if she sells shares worth Rs. 72,000 at a premium of 10% and the rest at a discount of 5%.
Let us first find the total number of shares bought by Mrs. Kulkarni and assume them as ‘x’.
We know that the actual cost of ‘x’ shares is $Rs.100x$, as each share costs Rs. 100.
But Mrs. Kulkarni bought these shares at a distance of 9% of the price, which means that Kulkarni has bought these shares for $\left( 100-9 \right)\%=91\%$ of the total price.
So, the cost incurred for Kulkarni for buying ‘x’ shares is 91% of $Rs.100x$.
We know that a% of b is defined as $\dfrac{a}{100}\times b$.
So, the cost of ‘x’ shares is $\dfrac{91}{100}\times 100x=Rs.91x$, which is equal to Rs. 1,31,040.
$\Rightarrow 91x=131040$.
$\Rightarrow x=1440$.
So, we have found that Mrs. Kulkarni bought 1440 shares each worth Rs. 100.
Mrs. Kulkarni sells shares worth Rs. 72,000 at a premium of 10%.
Now, let us find the total number of shares that are worth Rs. 72,000. Let us assume that number as ‘y’.
So, we have $100y=72000$.
$\Rightarrow y=720$. So, we have found that Mrs. Kulkarni is selling 720 shares at a 10% higher price.
So, the total price of these 720 shares is $\left( 100+10 \right)\%=110\%$ of Rs. 72000. Let us assume it as ${{P}_{1}}$.
$\Rightarrow {{P}_{1}}=\dfrac{110}{100}\times 72000=79200$ ---(1).
Now, Mrs. Kulkarni sells the remaining shares at a discount of 5%.
Let us find the total number of remaining shares.
The no. of remaining shares = $\left( 1440-720 \right)=720$, we know that these 720 shares are worth Rs. 72000 and these are selling at 5% lesser price.
So, the total price of these 720 shares is $\left( 100-5 \right)\%=95\%$ of Rs. 72000. Let us assume it as ${{P}_{2}}$.
$\Rightarrow {{P}_{2}}=\dfrac{95}{100}\times 72000=68400$---(2).
Let us find the total amount that Mrs. Kulkarni sold the shares. Let it be P.
So, we have $P={{P}_{1}}+{{P}_{2}}=Rs.79200+Rs.68400=Rs.147600$.
Now, let us subtract the cost incurred to Mrs. Kulkarni from P.
So, we get $P-C=Rs.147600-Rs.131040=Rs.16560$.
We can see the difference of selling price and cost price is positive, which means that Mrs. Kulkarni got a profit of Rs. 16560.
∴ The total gain in the whole is Rs. 16560.

Note: We should know that if they get the difference of selling price and cost price as negative, we incur loss. If we get it as zero, it tells us that there is no profit or loss. We can see that the given problem contains a lot of calculations which may lead us to make mistakes and confuse us. So, we need to calculate each step carefully. Similarly, we can expect problems to find the profit percentage incurred by Mrs. Kulkarni.