Correct Answer - Option 3 : 8 gm
Calculation:
Let the weight of the first metal be x.
Then the weight for other metal would be (18 - x).
Also, let the price of other metal be Rs. K per gram. We know that price for the first metal is Rs. 13.4.
∴ Now, the Price for the first metal = Rs. 13.4 per gram
Price for second metal = Rs. K per gram
Originally, the Weight of the first metal = x gm and weight of the second metal = (18 - x) gm
Also, originally worth of the lump = Rs. 174
∴ 13.4x + K (18 - x) = 174 ----(i)
When the weights are interchanged, the Weight of the first metal = (18 - x) gm and the Weight of the second metal = x gm
∴ 13.4 (18 - x) + Kx = 157.2 ----(ii)
Adding the two equations above:
13.4x + 18K – Kx + (13.4 × 18) - 13.4x + Kx = 174 + 157.2
⇒ 18K + 241.2 = 331.2
⇒ 18k = 90
⇒ K = 90/18
⇒ 10/2
⇒ 5
Substituting value of K = 5 in equation (i)
13.4x + (5 × (18 – X)) = 174
⇒ x = 10
Thus, the weight of other metal in the mixture = (18 - 10) gm
⇒ 8 gm
∴ the weight of other metal in the mixture is 8 gm.
