Question

The two numbers are in the ratio of 9:7.if the differnce of their square is 288.then the smaller of the number is
a) 2 b)24 c)27 d)28​

Answer 1

Let one number be 9M and other number be 7M.

Difference in the square of two numbers is 288.

According to question

Square of biggest number - Square of smaller number = 288

Let the -

• bigger number = 9M
• smaller number = 7M

→ (9M)² - (7M)² = 288

→ 81M² - 49M² = 288

→ 32M² = 288

→ M² = 9

→ M = $\pm$ 3

→ M = + 3

So,

Larger number = 9M

→ 9(3)

→ 27

Smaller number = 7M

→ 7(3)

→ 21

•°• Smaller number is 21 and larger number is 27

(Given options are wrong)

Answer 2

Suppose one no.( biggest no.)= 9M.

and other no.( Smallest no.) = 7M.

If the difference of their square is 288.

(9M)^2 - (7M)^2 = 288.

81M^2 '- 49M^2 = 288.

32M^2 = 288.

M^2 = 9 .

M = + 3.

M = +3.

Largest no. = 9M.

= 9(3)

= 27.

Smallest no. = 7M.

= 7(3)

= 21.