An investment index has 12 shares. Three of these shares, namely, R, H and F have weightage

[Mikrislac]

An investment index has 12 shares. Three of these shares, namely, R, H and F have weightage of 7%, 13% and 15% respectively. Over a period of two years, the prices of these shares rose by 9%, 10% and 4% respectively and the index rose by 6%. What was the increase in the prices of the remaining shares?

(A) 3.62 %

(B) 4.58 %

(C) 4.91 %

(D) 5.25 %

(E) 5.34 %

[Scott@TargetTestPrep]

An investment index has 12 shares. Three of these shares, namely, R, H and F have weightage of 7%, 13% and 15% respectively. Over a period of two years, the prices of these shares rose by 9%, 10% and 4% respectively and the index rose by 6%. What was the increase in the prices of the remaining shares?

(A) 3.62 %

(B) 4.58 %

(C) 4.91 %

(D) 5.25 %

(E) 5.34 %

Solution:

We can let the total value of the 12 shares = $100. Therefore, the values of shares R, H and F are $7, $13 and $15, respectively, while the remaining 9 shares have a total value of $65. We can create an equation where n is the percent increase of the remaining 9 shares:

7 x 1.09 + 13 x 1.1 + 15 x 1.04 + 65 x (1 + n/100) = 100 x 1.06

7.63 + 14.3 + 15.6 + 65 + 13n/20 = 106

102.53 + 13n/20 = 106

13n/20 = 3.47

n = 3.47 x 20/13 = 5.34

Answer: E

[Mikrislac]

Let the value of the index be 100. Then, the shares of R, H and F have the respective values: 7, 13 and 15. The remaining shares would have the value of 100 - (7 + 13 + 15) = 65.

Since the values of the shares rose by 9%, 10% and 4%, the new values of R, H, and F wil be 7.63, 14.3 and 15.60. The new value of the remaining shares then would be 68.47.

Hence, the required percentage increase in the value of the remaining shares equals (3.47/65)*100 = 5.34%.

[spoiler]Answer: (E)[/spoiler]

[deloitte247]

R = 7% of total investment
H = 13% of total investment
F = 15% of total investment
Let remaining shares = X
X = 100% - (13 + 7 + 15)%
X = 100% - 35%
X = 65%


Increase in R = 9%
Increase in H = 10%
Increase in F = 4%
Find an increase in X


Assuming that the whole investment index = $100
R = $7, H = $13, F = $15, X = $65
The whole index increased by 6% i.e it became => $100 + (6% of 100) = $106 out of which R = 7 + (9% of 7) = 7.63; H = 13 + (10% of 13) = 14.3; F =15 + (4% of 15) = 15.6
Total of the 3 = 7.63 + 14.3 + 15.6 = 37.53
X= 106 - 37.53 = 68.47


$$\%\ increase\ of\ X=\frac{increase}{original\ }\cdot\frac{100}{1}$$
$$=\frac{68.47-65}{65}\cdot\frac{100}{1}$$
$$=\frac{3.47}{65}\cdot\frac{100}{1}$$
$$=0.0534\cdot100$$
$$=5.43\%$$

$$Answer\ =\ E$$