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 would he have eaten during the week?

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

Answer 1

Answer: (A)

$99.22\%$

Pizza he ate on Monday $=\frac{1}{2}$
Pizza left $=\frac{1}{2}$
Pizza he ate on Tuesday $=\frac{1}{2}\times \frac{1}{2}=\frac{1}{4}$
Pizza left $=\frac{1}{2}-\frac{1}{2}=\frac{1}{4}$
Pizza he ate on Wednesday $=\frac{1}{2}\times \frac{1}{4}=\frac{1}{8}$
Pizza left $=\frac{1}{4}-\frac{1}{8}=\frac{1}{8}$
Continuing this pattern we see that
Pizza he ate on Thursday Friday Saturday and Sunday is $\frac{1}{16},\frac{1}{32},\frac{1}{64}$ and $\frac{1}{128}$ respectively
$\therefore$ Quantity of pizza ate during the week
$=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}$
$=\frac{64-32+16+8+4+2+1}{128}=\frac{127}{128}$
$=\frac{127}{128}\times 100\%$ $=99.22\%$