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A wine seller had three types of wine, 403 litres of 1st kind, 434 litres of 2nd kind and 465 litres of 3rd kind. Find the least possible number of casks of equal size in which different types of wine can be filled without mixing.
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- 46
- 44
- 42
- 48
Correct Option: C
For the least possible number of casks of equal size, the size of each cask must be of the greatest capacity. Hence, the capacity of the cask will be equal to the HCF of 403 l, 434 l and 465 l.
Now, HCF of 403 and 434.
Required HCF= HCF of 31 and 465
∴ Required HCF = 31 litres = Capacity of a cask.
| ∴ required number of casks = | + | + | 31 | 31 | 31 |
Hence , required number of casks = 13 + 14 + 15 = 42
