ACT Practice Paper2 Solution2

In this page ACT practice paper2 solution2 we are going to see solution of some practice questions.

Question 5:

The ratio of three numbers is 3 : 4 : 5 and the sum of their squares is 1250. The sum of the numbers is.

Solution:

Let the three numbers are 3 x,4 x and 5 x

sum of their squares = 1250

(3 x)² + (4 x)² + (5 x)² = 1250

9 x² + 16 x² + 25 x ² = 1250

50 x² = 1250

    x² = 1250/50

    x² = 25

    x = √25

    x = √5 x 5

    x = 5

3 x = 3 (5) = 15

4 x = 4 (5) = 20

5 x = 5 (5) = 25

Therefore the required three numbers are 15,20,25

Sum of three numbers = 15 + 20 + 25

                              = 60

The required answer is 60. So option C is correct.


Question 6:

David is younger than Daniel by 4 years. If their ages are in the respective ratio of 7 : 9, how old is David?

Solution:

Here age of David is compared by using age of Daniel.

Let “x” be the age of Daniel

So “x – 4” be the age of David

Their ages are in the ratio 7 : 9

 (x – 4) : x = 7 : 9

(x - 4)/x = 7/9

9 (x – 4) = 7 x

9 x – 36 = 7 x

9 x – 7 x = 36

2 x = 36

   x = 36/2

   x = 18

x – 4 = 18 – 4 = 14

Therefore the age of David is 18


5^(x + 3) = 25 ^(3 x – 4), then the value of x is

Solution:

Now we are going to write 25 as 5²

5^(x + 3) = 5^2(3 x – 4)

Here bases are equal in both sides. So we can equalize the powers

x + 3 = 2 (3 x – 4)

x + 3 = 6 x – 8

x – 6 x = -8 – 3

-5x = -11

   x = 11/5

ACT practice paper2 solution2 ACT practice paper2 solution2