A person buys national savings certificate of values exceeing of the last years purchase by Rs. 100. after 12years he finds that the total value of certificate purchased by him is Rs. 7,200 find the value of the certificate purchased by him (1) in the first year and (2) in the eighth year.
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To solve this problem, let's use a systematic approach.
Step 1: Define the variables:
Let's assume the value of the certificate purchased in the first year is 'x' (in Rs.).
Step 2: Understand the given information:
According to the problem, the person buys national savings certificates in increasing values compared to the previous year's purchase. After 12 years, the total value of all the certificates purchased is Rs. 7,200.
Step 3: Set up the equation:
To find the solution, we need to set up an equation based on the given information.
In the first year, the person purchased certificates worth 'x' (as given). So, the value of the certificate purchased in the second year will be 'x + Rs. 100' (as there is an increase of Rs. 100 from the previous year).
Similarly, the value of the certificate purchased in the third year will be '(x + Rs. 100) + Rs. 100'.
In this way, the value of the certificate purchased in the 12th year will be [x + (12 - 1) * Rs. 100].
Now, let's sum up the values of all the certificates purchased in 12 years:
x + (x + Rs. 100) + (x + Rs. 100 + Rs. 100) + ... [up to 12 terms]
The sum of these terms is given as Rs. 7,200.
Therefore, the equation is:
x + (x + Rs. 100) + (x + Rs. 100 + Rs. 100) + ... + [x + (12 - 1) * Rs. 100] = Rs. 7,200
Step 4: Simplify and solve the equation:
By simplifying the equation, we get:
12x + 66 * Rs. 100 = Rs. 7,200
Step 5: Solve for 'x':
Simplifying further, we have:
12x + Rs. 6,600 = Rs. 7,200
12x = Rs. 7,200 - Rs. 6,600
12x = Rs. 600
x = Rs. 50
Therefore, the value of the certificate purchased in the first year is Rs. 50.
Step 6: Find the value of the certificate purchased in the eighth year:
To find the value of the certificate purchased in the eighth year, we can use the equation:
Value of the certificate in the eighth year = x + (8 - 1) * Rs. 100
Substituting the value of 'x' as Rs. 50, we have:
Value of the certificate in the eighth year = Rs. 50 + 7 * Rs. 100
Value of the certificate in the eighth year = Rs. 50 + Rs. 700
Value of the certificate in the eighth year = Rs. 750
Therefore, the value of the certificate purchased in the eighth year is Rs. 750.
So, the answers to the questions are:
(1) The value of the certificate purchased in the first year is Rs. 50.
(2) The value of the certificate purchased in the eighth year is Rs. 750.