The three scales below are perfectly balanced if • = 3. What are the values of ∆ and *?
A.

B.

C.

Question

The three scales below are perfectly balanced if • = 3. What are the values of ∆ and *?A. B. C.

Philoid · Accepted Answer

Let the value of Δ and * be x and y, respectively and it is given that • = 3.

From (a), y + y + y + y + y = x + x + 3 + 3

⇒ 5y = 2x + 6

⇒ 5y – 2x = 6

⇒ 2x – 5y = –6 … (1)

From (b) x + x = y + y + 3 + 3

⇒ 2x = 2y + 6

⇒ 2x – 2y = 6

⇒ x – y = 3 [dividing both sides by 2] …. (2)

From (c), y + y + y + 3 + 3 + 3 = x + x + x

⇒ 3y + 9 = 3x

⇒ 3x – 3y = 9

⇒ x – y = 3 [Dividing both sides by 3] … (3)

From eq. (3) x – y = 3

⇒ x = y + 3

On putting x = y + 3 in Eq (1), we get

⇒ 2(y + 3) – 5y = –6

⇒ 2y + 6 – 5y = –6

⇒ –3y = –6 – 6

⇒ –3y = – 12

⇒ [Dividing both sides by –3]

⇒ y = 4

On putting y = 4 in eq (3) we get

x = y + 3

⇒ x = 4 + 3 = 7

∴ value of Δ = x = 7 and value of * = y = 4