a perso buys national savings certificate values exceeding of the last years purchase by ₨.100.after 12 year he finds that the total value of certificate purchased by him ₨.7,200. find the value of the certificate purchase by him (1) in the first year and (2) in the eighth year.
clearly a geometric series. What do you know about them?
please sir
Surely by now you have some idea how to write the words in algebra. If last year's certificate was worth Rs a, then
ar = a + 100
ar^12 = 7200
Now go to work on that.
To solve this problem, we can break it down into two parts: finding the value of the certificate purchased in the first year (part 1) and finding the value of the certificate purchased in the eighth year (part 2).
Let's start with part 1:
Let's assume the value of the certificate purchased in the first year is "X" rupees.
According to the given information, the person buys national savings certificates values exceeding the last year's purchase by ₨.100. It means that the person buys the certificate in the second year at a value of (X + 100) rupees.
Similarly, in the third year, the value of the certificate would be (X + 100) + 100 = (X + 200) rupees.
In general, we can express the value of the certificate purchased in the n-th year as (X + (n - 1) * 100) rupees.
Since the person holds the certificate for 12 years, we can set up the following equation to represent the total value of all the certificates purchased over the 12 years:
X + (X + 100) + (X + 200) + ... + (X + 11 * 100) = ₨.7,200
To simplify the equation, we can rewrite it as:
12X + 10 * 100 * 6 = ₨.7,200
12X + 6000 = ₨.7,200
12X = ₨.1,200
Dividing both sides of the equation by 12 gives:
X = ₨.100
Therefore, the value of the certificate purchased in the first year is ₨.100.
Now, let's move on to part 2:
We need to find the value of the certificate purchased in the eighth year.
Using the same formula we derived earlier, the value of the certificate purchased in the n-th year is given by (X + (n - 1) * 100).
So, in the eighth year, the value would be ₨.100 + (8 - 1) * 100 = ₨.800.
Therefore, the value of the certificate purchased in the eighth year is ₨.800.