Question

Mohan ate half a pizza 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 pizza (in percentage) would he have eaten during the week?

• A. $99.22\%$
• B. $95\%$
• C. $98.22\%$
• D. $100\%$

Answer 1

Answer: (A)

$99.22\%$

Mohan ate $\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}$ of the pizza during the week.
The above sequence is a geometric progression with
first term, $a=\frac{1}{2}$, common ratio, $r=\frac{1}{2}$ and number of terms, $n=7$
$\therefore$ The sum of this G.P is
$\frac{\frac{1}{2}[1-{\left(\frac{1}{2}\right)}^7]}{1-\frac{1}{2}}=1-\frac{1}{128}=\frac{127}{128}$
$=$ $99.22\%$