Question

Question 106

The three scales below are perfectly balanced, if $\cdot =3.$ What are the values of $△\text{and}\ast$?

Answer 1

Let the value of $△\text{and}\ast$ be x and y, respectively and it is given that $\cdot =3.$
From (a), y + y + y + y + y = x + x + 3 + 3
$\Rightarrow 5y=2x+6$
$\Rightarrow 5y-2x=6$
$\Rightarrow 2x-5y=-6.....\left(i\right)$
From (b), x + x = y + y + 3 + 3
$\Rightarrow 2x=2y+6$
$\Rightarrow 2x-2y=6$
$\Rightarrow x-y=3$
From(c), y + y + y + 3 + 3 + 3 = x + x + x
$\Rightarrow 3y+9=3x\Rightarrow 3x-3y=9\Rightarrow x-y=3\left[\text{dividing both sides by 2}\right]...\left(ii\right)$
From Eq. (iii), x - y = 3 $\Rightarrow$ x = y + 3
On putting x = y + 3 in Eq. (i), we get
2(y+3) - 5y = -6
$\Rightarrow 2y+6-5y=-6-3y+6=-6\Rightarrow -3y=-6-6=-12y=\frac{-12}{-3}=4$
On putting y = 4 in Eq.(ii), we get x - y = 3
$\Rightarrow x-4=3\Rightarrow x=3+4=7\Rightarrow x=7$
$\therefore △=x=7\text{and value of}\ast =y=4.$