Discussion

Explanation:

Total weight of the final mixture = 12 + 6 = 18 kgs.

Suppose x kg is taken from A.

Then, (18 – x) kg is taken from B. 

${\frac{5}{8}}^{th}$ of the mixture in A and ${\frac{7}{10}}^{th}$ of the mixture in B is iron. 

∴ $\frac{5}{8}x$ + $\frac{7}{10}$(18 – x) = 12

Hence, x = 8

⇒ 8 kg must be taken from A and 10 kg must be taken from B.

Alternately,
Fraction of iron in A = $\frac{5}{8}$, in B = $\frac{7}{10}$ and in the final mixture = $\frac{2}{3}$

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∴ $\frac{\mathrm{Quantity} \mathrm{of} \mathrm{A}}{\mathrm{Quantity} \mathrm{of} \mathrm{B}}$ = $\frac{1/24}{1/30}$ = $\frac{4}{5}$

Total quantity of A an B = 12 + 6 = 18 kgs.

∴ Quantity of A = $\frac{4}{9}$× 18 = 8 kgs.

Hence, option (c).

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