| An alloy of steel contains iron and carbon in the ratio 3: 4. If 120 kg of iron is added to the alloy, then the same ratio become 5: 4. Find the initial quantity of iron in the alloy. |
A) 175 kg
B) 180 kg
C) 160 kg
D) 185 kg
Correct Answer: B
Solution :
| Given, \[\frac{\text{Iron}\,\text{(}l\text{)}}{\text{Carbon}\,\text{(}C\text{)}}=\frac{3}{4}\] |
| \[\Rightarrow \] \[4\times l=3C\]\[\Rightarrow \]\[C=\frac{4l}{3}\] (i) |
| and \[\frac{l+120}{C}=\frac{5}{4}\]\[\Rightarrow \]\[\frac{l+120}{\frac{4l}{3}}=\frac{5}{4}\] [from Eq.(i)] |
| \[\Rightarrow \] \[\frac{3\,(l+120)}{4l}=\frac{5}{4}\]\[\Rightarrow \]\[\frac{3\,(l+120)}{l}=\frac{5}{1}\] |
| \[\Rightarrow \] \[3l+360=5l\]\[\Rightarrow \]\[5l-3l=360\] |
| \[\Rightarrow \] \[2l=360\]\[\Rightarrow \]\[l=\frac{360}{2}=180\] |
| Hence, initial quantity of iron in the alloy is 180 kg. |
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