Question

[1] Two numbers are in the ratio 2:3
and the difference of their squares is
320. The numbers are :
(a) 12, 18
(b) 16, 24
(c) 14, 21
(d) None.​

Answer 1

Answer:

b) 16 , 24

Explanation:

(3X)^2 - (2X)^2 = 320

9X^2 - 4X^2 = 320

5X^2 = 320

X^2 = 64

X = 8

3X = 24 ; 24 / 8 = 3

2X = 16 ; 16 / 8 = 2

24^2 = 576

16^2 = 256

576 - 256 = 320

The numbers are 16 and 24

Answer 2

Answer:

Option b) 16,24

The numbers are 16 and 24.

Step-by-step explanation:

Consider the original numbers as :

• One as 2y
• Second as 3y

Their squares =

• First number = (2y)² = 4y²
• Second number = (3y)² = 9y²

___________________

⇒ 9y² - 4y² = 320

⇒ 5y² = 320

⇒ y² = 320/5

⇒ y² = 64

⇒ y = √64

⇒ y = 8

___________________

First number :

⇒ 2(8)

⇒ 16

First number is 16.

___________________

Second number :

⇒ 3(8)

⇒ 24

Second number is 24.

Therefore, the numbers are 16 and 24.