Question : Raju ate $\frac{3}{8}$th part of a pizza and Adam ate $\frac{3}{10}$th part of the remaining pizza. Then Renu ate $\frac{4}{7}$th part of the pizza that was left. What fraction of the pizza is still left?
Option 1: $\frac{5}{12}$
Option 2: $\frac{1}{4}$
Option 3: $\frac{1}{8}$
Option 4: $\frac{3}{16}$
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Correct Answer: $\frac{3}{16}$
Solution :
Let the total pizza be 1 part.
Raju ate $\frac{3}{8}$th part of it.
Remaining Part of the pizza $=(1 - \frac{3}{8})=\frac{5}{8}$ part
Adam ate $\frac{3}{10}$th part of the remaining pizza.
So, Adam ate $(\frac{5}{8} × \frac{3}{10}) = \frac{15}{80} = \frac{3}{16}$ part of the total pizza
Total pizza is eaten $(\frac{3}{8} + \frac{3}{16})=\frac{9}{16}$ part
Remaining pizza $=(1 - \frac{9}{16})=\frac{7}{16}$ part
Then Renu ate $\frac{4}{7}$th part of the pizza.
Renu ate $(\frac{7}{16} × \frac{4}{7}) = \frac{1}{4}$ part of the pizza
Together they ate $(\frac{3}{8} + \frac{3}{16} + \frac{1}{4})=\frac{13}{16}$ part
Final remaining pizza $=(1 - \frac{13}{16})=\frac{3}{16}$ part
Hence, the correct answer is $\frac{3}{16}$.
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