Question

Sanjana's hobby includes collecting sea-shells. From $2009$ to $2010$, Sanjana increased her collection of sea shells by $30\%$. From $2010$ to $2012$, she added another $20\%$ to her collection. But in $2014$, she had to move away and get rid of $50\%$ of her collection. At the end, what percent of the sea shells did Sanjana have with her?

• A. $75$
• B. $78$
• C. $100$
• D. $150$
• E. $156$

Answer 1

The correct option is B $78$

Let sea shells with Sanjana be $100$
From $2009-10$ she added $30\%$ to her collection,
Number of shells stood to $100+\frac{30}{100}\times 100=130$
From $2010$ to $2012$ she added another $20\%$ to her collection, her collection stood to
$130+\frac{20}{100}\times 130=130+26=156$
But in $2014$ she had to move away and get rid of $50\%$ of her collection, so sea shells remaining with her are $=$ $\frac{50}{100}\times 156=78$ shells.
Percentage of sea shells sanjana have with her are $=$ $\frac{78}{100}\times 100=78$.