# 80 investors were surveyed. All investors had either 1 mutual fund or 2 stocks.50 had 1 mutual fund, and 55 had 2 stocks . How many investors had 1 mutual fund and 2 stocks?

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Here we have to use set theory. Now the total number of investors surveyed is 80. All the investors have either one mutual fund or two stocks.

The total number of investors is equal to those who have one mutual fund plus those who have two stocks minus those who have both a mutual fund as well as two stocks.

The number of investors with one mutual fund is 50. The number of investors with two stocks is 55.

Now 80 is equal to the number of investors with two stocks + number of investors with one mutual fund - number of investors with both a mutual fund and two stocks.

80 = 50 + 55 - N

=> N = 50 + 55 - 80

=> N = 25

**Therefore 25 investors have both 2 stocks as well as 1 mutual fund.**

We represent the entire set of investors as I.

Let M be the set mutual fund investors. Let S be the set of ivstors in stocks.

Then I = MUS

The number of investors = n(I) = 80.

the number of investors in mutual fund = n(M) = 50.

The number of investors in stocks = n (S) = 55.

Therefore, I = M U S

n(NUS) = n(M) +n(m) - n(N & S).....................(1), where (N&S) represents set of investors investing in both N and S

Therefore , from(1) , we get: n(N&S) = n(M) + n(S) - n(M U S).

Given that n(MUM) = 80 , n(M ) = 50 , n(S) = 55,

Therefore n(M &S) = 50+55-80 = 105-80 = 25.

Therefore there are 25 investors who invested in both mutual fund and stocks.