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Ram ate half a cheese on Monday he ate half of what was left on Tuesday and so on. He followed this pattern for one week. How much of the cheese would he have eaten during the week?
- A99.22%
- B95%
- C98.22%
- D100%
Answer not set
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Summation of a G.P.$(= \frac{{a\left( {1 - {r^n}} \right)}}{{1 - r}})$
Where a is starting term and r is multiplication factor.
Given, Ram ate half a cheese on Monday he ate half of what was left on Tuesday and so on.
Amount of cheese eaten by Ram $(= \frac{1}{2} + \frac{1}{2} \times \frac{1}{2} + \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \ldots \ldots ..\; + {\frac{1}{2}^7})$
⇒ Amount of cheese eaten by Ram $(= \frac{1}{2} \times \frac{{1 - \frac{1}{{{2^7}}}}}{{1 - \frac{1}{2}}})$
⇒ Amount of cheese eaten by Ram $(= \frac{1}{2} \times \frac{{1 - \frac{1}{{128}}}}{{\frac{1}{2}}} = \frac{{127}}{{128}} = 0.9922)$
∴ Amount of cheese eaten by Ram in% = 99.22%
Where a is starting term and r is multiplication factor.
Given, Ram ate half a cheese on Monday he ate half of what was left on Tuesday and so on.
Amount of cheese eaten by Ram $(= \frac{1}{2} + \frac{1}{2} \times \frac{1}{2} + \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \ldots \ldots ..\; + {\frac{1}{2}^7})$
⇒ Amount of cheese eaten by Ram $(= \frac{1}{2} \times \frac{{1 - \frac{1}{{{2^7}}}}}{{1 - \frac{1}{2}}})$
⇒ Amount of cheese eaten by Ram $(= \frac{1}{2} \times \frac{{1 - \frac{1}{{128}}}}{{\frac{1}{2}}} = \frac{{127}}{{128}} = 0.9922)$
∴ Amount of cheese eaten by Ram in% = 99.22%