Question

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

a.
b.
c.

Answer 1

Given that • = 3  ...(i)

1. 5* = 2Δ + 2•  ...(ii)
2. 2Δ = 2* + 2•  ...(iii)
3. 3* + 3• = 3Δ  ...(iv)

Putting the value of (iii) in (ii), we get

5* = 2* + 2• + 2•

⇒ 5* – 2* = 4•

⇒ 3* = 4 × 3  ...[Using (i)]

⇒ * = `(4 xx 3)/3` = 4

Putting the value of * and • in (iv), we get

3 × 4 + 3 × 3 = 3Δ

⇒ 3Δ = 21

⇒ Δ = `21/3`

⇒ Δ = 7