Question

$20+\frac{2}{5}+\frac{1}{4}+\frac{2}{3}+\frac{1}{2}=?$

• A. $\frac{1309}{16}$
• B. $\frac{1309}{14}$
• C. $20\frac{49}{60}$
• D. $29\frac{49}{60}$
  

Answer 1

Answer: (D)

Given:

$20+\frac{2}{5}+\frac{1}{4}+\frac{2}{3}+\frac{1}{2}$

$\begin{array}{cc}2& 2,3,4,5\\ 2& 1,3,2,5\\ 3& 1,3,1,5\\ 5& 1,1,1,5\\ & 1,1,1,1\end{array}$

LCM of $5,4,3$ and $2$ is $2\times 2\times 3\times 5=60$
$=20+\frac{2\times 12}{5\times 12}+\frac{1\times 15}{4\times 15}+\frac{2\times 20}{3\times 20}+\frac{1\times 30}{2\times 30}$

$=20+\frac{24}{60}+\frac{15}{60}+\frac{40}{60}+\frac{30}{60}$

$=20+\frac{109}{60}$

$=\frac{1200+109}{60}$

$=\frac{1309}{60}$

$=21\frac{49}{60}$

Hence, Option A is correct.