Question

On Monday, the value of a company's shares was Rs.7.50. The price increased by 6% on Tuesday, decreased by 1.5% on Wednesday, and decreased by 2% on Thursday. Find the value of each share when trade opened on Friday.

Answer 1

Hint: The increase of 6% on Tuesday will give the new price as Rs.\[7.50\left( 1+\dfrac{6}{100} \right)\]. Similarly, find the price on Friday using this method. To get the required answer.
Complete step by step solution:
In the question, we have to find the value of each share when trade opened on Friday, if it is given that on Monday, the value of a company's shares was Rs.7.50. The price increased by 6% on Tuesday, decreased by 1.5% on Wednesday, and decreased by 2% on Thursday.
Now, the price of the company's shares on Monday was Rs.7.50.
On Tuesday there was an increase of 6% on the share’s price than that of on Monday. So here the new share’s price on Tuesday will be given by:
 \[\begin{align}
  & \Rightarrow 7.50+7.50\times \left( \dfrac{6}{100} \right) \\
 & \Rightarrow 7.50\left( 1+\dfrac{6}{100} \right) \\
\end{align}\]
Next, on Wednesday, the share price decreased by 1.5% of the previous day i.e., Tuesday.
So here the new share’s price on Wednesday will be given by:
\[\begin{align}
  & \Rightarrow 7.50\left( 1+\dfrac{6}{100} \right)+7.50\left( 1+\dfrac{6}{100} \right)\left( -\dfrac{1.5}{100} \right) \\
 & \Rightarrow 7.50\left( 1+\dfrac{6}{100} \right)-7.50\left( 1+\dfrac{6}{100} \right)\left( \dfrac{1.5}{100} \right) \\
 & \Rightarrow 7.50\left( 1+\dfrac{6}{100} \right)\left( 1-\dfrac{1.5}{100} \right) \\
\end{align}\]
Similarly, on Thursday the price again is decreased by 2% then the previous day i.e., Wednesday.
So here the new share’s price on Thursday will be given by:
\[\begin{align}
  & \Rightarrow 7.50\left( 1+\dfrac{6}{100} \right)\left( 1-\dfrac{1.5}{100} \right)\left( 1-\dfrac{2}{100} \right) \\
 & \Rightarrow 7.50\left( 1+0.06 \right)\left( 1-0.015 \right)\left( 1-0.02 \right) \\
 & \Rightarrow 7.50\left( 1.06 \right)\left( 0.985 \right)\left( 0.98 \right) \\
 & \Rightarrow 7.674135 \\
\end{align}\]
Here, we have to round it to two digits after decimal to get the price. So we have:
\[\Rightarrow 7.674135\approx 7.67\]
Finally, the share price when trade opened on Friday will be the same as the price at the end of Thursday and that is Rs. 7.67 per share.

Note: Be careful when it says that the price has been increased or decreased by some percentage. Here, the increase or decrease is always from the previous price. Also, note that the share price at the end of any day will be the same as the price at the opening of the next day.