# Difficult Percentages Solved QuestionAptitude Discussion

 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

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.