The investors can invest in four mutual funds – ICICI, SBI, Kotak and HDFC, to buy stocks of these four companies. Not all the investors invested in the mutual funds every month but when they did, each person invested Rs.100 to any one of the four mutual funds in a month, not necessarily the same fund every month.
For each of the four funds, the number of people who invested in each of October, November and December was either equal to or one greater or one lesser than their corresponding numbers in the previous month. For example, if ‘n’ investors invested in the ICICI fund in October, then the number of investors who invested in the ICICI fund in November can be ‘n – 1’, or ‘n’ or ‘n + 1’.
The following bar graph shows the average amount invested in each fund in each of the four months. The average in a given month is defined as the total amount invested in the fund till that month (including that month) divided by the maximum number of investors who have invested in the fund in any month up-to that month (including that month).
Q.1 What was the total amount invested by the investors in all the four mutual funds combined in December?
ICICI
Let the number of investors who invested in ICICI fund in September be ‘n’
So the number of investors who invested in ICICI fund in October will be also n, since the average upto October is 100.
Now we can see that the average has reduced in November. Hence we can infer that the number of investors has changed. It can either be n+1 or n-1.
Case I
If the number of investors is n+1, then
283.33 = [100n + 100n + 100(n+1)]/n+1
283.33n + 283.33 = 300n +100
183.33 = 16.66n
n=11
Then the number of investors in September, October & November would be 11, 11 & 12 respectively.
So the number of investors in December could be 11, 12 or 13.
If the number of investors in December is 11 or 12, the total amount invested in ICICI fund in the four months would be 350*12 = Rs 4200(since the maximum number of investors in any month would be 12).
So the amount invested in December in ICICI fund will be 4200 –[(11+11+12)100] = Rs800
Hence the number of investors who invested in December cannot be 11 or 12.
If the number of investors in December is 13, the total amount invested in ICICI fund in the four months would be 350*13 = Rs 4550(since the maximum number of investors in any month would be 13).
So the amount invested in December in ICICI fund will be 4550 –[(11+11+12)100] = Rs1150
Hence the number of investors who invested in December also cannot be 13.
Case II
If the number of investors is n-1, then
283.33 =[100n + 100n + 100(n-1)]/n
283.33n = 300n -100
100=16.66n
n=6
Then the number of investors in September, October & November would be 6, 6 & 5 respectively.
So the number of investors in December could be 4, 5 or 6.
If the number of investors in December is 4,5 or 6, the total amount invested in ICICI fund in the four months would be 350*6 = Rs 2100(since the maximum number of investors in any month would be 6).
So the amount invested in December in ICICI fund will be 2100 –[(6+6+5)100] = Rs400
Hence the number of investors who invested in December will be 4.
Similarly we can fill the rest of the table
Answer 1) Rs. 1800
Investors who invested in December= 4+5+6+3= 18 . Hence the total amount invested =18×100= Rs.1800
Q.2 What was the maximum number of investors who invested to any fund in any month?
Answer 2) 8
From the table we can observe that 8 investors contributed to SBI in September.
Q.3 If each investor invested to a fund only once in these four months, what can be the maximum number of investors who invested in the four months?
Answer 3) 81
Since the number of investors has to be maximum possible, we can add all the values in the table which will give us 81 as the answer.
Q.4 What was the maximum contribution (in Rs.) to any fund over the given four month period?
Answer 4) Rs. 2600
Maximum amount was invested in SBI over the given four month period.
Total amount = (8+7+6+5)x100 = Rs. 2600
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