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Progressions - Quant/Math - CAT 2009
Question 4 the day:
June 3, 2003
The question for the day is from the topic of Progressions.
- A gentleman buys every year Bank's cash certificates of value exceeding the last year's purchase by Rs. 300. After 20 years, he finds that the total value of the certificates purchased by him is Rs. 83,000. Find the value of the certificates purchased by him in the 13th year.
| (1) |
Rs. 4900 |
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(2) |
Rs. 6900 |
| (3) |
Rs. 1300 |
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(4) |
None of these. |
Correct Answer - (1)
Solution:
Let the value of the certificates purchased in the first year be Rs. a.
The difference between the value of the certificates is Rs. 300 (d = 300).
Since, it follows Arithmetic progression the total value of the certificates after 20 years is given by
Sn = n/2 [2a + (n - 1) d] = 20/2[2a + 19(300)] = 83,000.
By simplifying we get 2a + 5700 = 8300.
Therefore, a = Rs. 1300.
The value of the certificates purchased by him in nth year = a + (n - 1) d.
Therefore, the value of the certificates purchased by him in 13th year = 1300 + (13 - 1) 300 = Rs. 4900.
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