Q) the value of particular stock increased by 10% everyday for first four days a week. However its value decreased by 30% at the end of the fifth day compared to its value at the end of the fourth day. if at the end of the fifth day the value of the stock was $56. what was the value of stock at the end of second day?
Options) a) $66.11 b) $72.73 c) $54.64 d) $60.1
My progress:
So what I did is first calculated the 10% for X (x = Some stock value) which is 0.1x, So I added that to X for day 1 = 1.1x.
So for 4 days (4 * 1.1x) = 4.4x
Now for 30% decrease on day 5, I calculated 30% of stock value till yet i.e 4.4x and it was 1.32x, Then I subtracted it with the stock value so it became => 4.4x – 1.32x = 3.08x
Now when the stock value is given and i try to calculate the value for 2nd day like this => 2.2(56) the answer is not even coming close to the options, I know I'm doing the last step wrong or But I'm unsure about what to do next.
Please guide me with some explanation and tell me where am I making the mistake.
Thanks.
Best Answer
Usually, you have to try to convert word problems into equations which you can solve easily.
For the first $4$ days, the stock value increases by $10$%, so you can write an equation for it. Let $v_n$ represent the stock value at the end of the $n^{th}$ day.
$$\color{blue}{v_4 = v_1(1.1)^4} \tag{1}$$
On the $5^{th}$ day, however, the stock value falls by $30$%, which means the stock value is $70$% of what it was on the previous day.
$$v_5 = 0.7v_4 \tag{2}$$
Applying $(1)$ to $(2)$, you get
$$v_5 = 0.7\color{blue}{\big[v_1(1.1)^4\big]}$$
Just let $v_5 = 56$.
$$56 = 0.7\big[v_1(1.1)^4)\big]$$
$$80 = v_1(1.1)^4$$
$$v_1 = \frac{80}{(1.1)^4}$$
You know that $v_2 = 1.1v_1$, so you get
$$v_2 = \frac{80}{(1.1)^4}\cdot 1.1 = \frac{80}{(1.1)^3} \approx 60.10581 \approx 60.11$$