Your friend plants a tree of height $1\frac{1}{3}ft$. After one year, the height of the tree increased by $1\frac{5}{6}ft$. After $2$ years, the height of the tree is $4\frac{11}{12}ft$. What is the increase in the height of the tree in the second year?

The correct option is A $1\frac{9}{12}ft$
Detailed step-by-step solution:
The height of the tree before planting $=1\frac{1}{3}\text{ft}$
The increase in its height in $1$ year $=1\frac{5}{6}\text{ft}$
The height of the tree after $2$ years $=4\frac{11}{12}\text{ft}$
The actual increase in the height of the tree in $2$ years $=$ Total height of the tree $-$ Height of the tree before planting
$=4\frac{11}{12}\text{ft}-1\frac{1}{3}\text{ft}$
$=\frac{4\times 12+11}{12}\text{ft}-\frac{1\times 3+1}{3}\text{ft}=\frac{59}{12}\text{ft}=\frac{59}{12}\text{ft}-\frac{4\times 4}{3\times 4}\text{ft}$
$=\frac{59}{12}\text{ft}-\frac{16}{12}\text{ft}$
$=\frac{59-16}{12}\text{ft}=\frac{43}{12}\text{ft}$
The increase in the height of the tree in the second year $=$ Increase in $2$ years $-$ Increase in the first year
$=\frac{43}{12}\text{ft}-1-\frac{5}{6}\text{ft}=\frac{43}{12}\text{ft}-\frac{1\times 6+5}{6}\text{ft}=\frac{43}{12}\text{ft}-\frac{11}{6}\text{ft}=\frac{43}{12}\text{ft}-\frac{11\times 2}{6\times 2}\text{ft}=\frac{43-22}{12}\text{ft}=\frac{21}{12}\text{ft}=1\frac{9}{12}\text{ft}$
Hence, option B is correct.