A container holds three liquids X, Y, and Z in the ratio 3 : 4 : 5. If 8 liters of X, 10 liters of Y, and a certain amount of Z are added, the new ratio becomes 7 : 9 : 12 . Find the quantity (in liters) of Z added.

Question

Accepted Answer

1. Let the initial amounts be $3k,4k,5k$. After adding we have $3k+8,\;4k+10,\;5k+z$.  
2. Use the first two parts: $\frac{3k+8}{4k+10}=\frac{7}{9}$. Solving gives $k=2$.  
3. So initial amounts are $6,8,10$. After adding they become $14,18,10+z$. The scale factor is $14/7=2$, so the third part must be $12	imes2=24$.  
4. Thus $10+z=24$ and $z=14$.

FINAL_ANSWER: b

Answer

Answer

Answer