Ganguly distributes 450 gifts among 4 children. The gifts received by the first child, twice the gifts received by the second child, three times the gifts received by the third child and four times the gifts received by the fourth child are all equal. How many gifts did the fourth child receive?
54
Let the common value be k, so the first child gets k, the second gets \(\frac{k}{2}\), the third gets \(\frac{k}{3}\) and the fourth gets \(\frac{k}{4}\).
Total: \(k\left(1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4}\right) = \frac{25k}{12} = 450\), so k = 216.
The fourth child gets \(\frac{216}{4} = 54\) gifts.
Hence, 54.
Similar Questions
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