Percentages
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Q.

Each person in a group of 110 investors has investments in either equities or securities or both. Exactly  $25%$  of  the  investors  in  equities  have  investments  in  securities,  and  exactly  $40%$  of  the investors in securities have investments in equities. How many have investments in equities?

 A.

60

 B.

80

 C.

70

 D.

90

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Solution:
Option(B) is correct

The investors can be categorized into three groups:

(1) Those who have investments in equities only.
(2) Those who have investments in securities only.
(3) Those who have investments in both equities and securities.

Let $x$, $y$, and $z$ denote the number of people in the respective categories. Since the total number of investors is 110, we have

$x + y + z = 110$ ------------- (1)

Also,
The number of people with investments in equities is $x + z$ and

The number of people with investments in securities is $y + z$.

Since exactly $25\%$ of the investors in equities have investments in securities, we have the equation

\(\dfrac{25}{100}\times (x+z)=z\)

\(\dfrac{25}{100}\times x= \dfrac{25}{100}\times z\)

\(x = 3z\) ------------------- (2)

Since exactly $40\%$ of the investors in securities have investments in equities, we have the equation

\(\dfrac{40}{100}\times (y+z)=z\)

\( (y+z)=\dfrac{5z}{2}\)

\( y=\dfrac{3z}{2}\)

Substituting equations (2) and (3) into equation (1) yields

\(3z+\dfrac{3z}{2}+z=110\)

\(\dfrac{11z}{2}=110\)

\(z=110\times \dfrac{2}{11}=20\)

Hence, the number of people with investments in equities is:

$x+z=3z+z=3×20+20=60+20$= 80


(1) Comment(s)


Jon Snow
 ()

how can they give options more than 110 so 2 options eliminated straight away also 65 is not completely divisible by 4 so remaining option is 80 which we get directly.