Q. 1065.0( 2 Votes )

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

A.

B.

C.

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


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