Discussion

Question:

The student fest in an Engineering College is to be held in one month’s time and no sponsorship has yet been arranged by the students. Finally the General Secretary (GS) of the student body took the initiative and decided to go alone for sponsorship collection. In fact, he is the only student doing the fund raising job on the first day. However, seeing his enthusiasm, other students also joined him as follows: on the second day, 2 more students join him; on the third day, 3 more students join the group of the previous day; and so on. In this manner, the sponsorship collection is completed in exactly 20 days. If an MBA student is twice as efficient as an Engineering student, the number of days which 11 MBA students would take to do the same activity , is:

Explanation:

Let engineering student collects fund of Rs. X on one day.

Number of students collecting funds on:

First day = 1

Second Day = 1 + 2

…

Twentieth day = 1 + 2 + 3 + 4 … + 20

Total collection = [1 + (1 + 2) + (1 + 2 + 3) + … + (1 + 2 + 3 + … + 20)] X

= $\sum_{i = 1}^{20} \frac{n (n + 1)}{2}$ = $\frac{1}{2}$ $\{\sum_{i = 1}^{20} n^{2} + \sum_{i = 1}^{20} n\}$ ...(i)

∑ $n^{2}$ = $\frac{n (n + 1) (2 n + 1)}{6}$ and

∑n = $\frac{n (n + 1)}{2}$

Thus, from equation (i),
Total collection

= $\frac{1}{2}$ $\{\frac{20 (20 + 1) (2 \times 20 + 1)}{6} + \frac{20 (20 + 1)}{2}\}$

= 1540X

An MBA student collects 2X on a single day.

∴ Number of days required for 11 MBA students to complete the activity

= 1540X / 11 × 2X = 70

Hence, option (a).

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