Question

The value of \({\dfrac{1\dfrac{1}{4}\div1\dfrac{1}{2}}{\dfrac{1}{15}+1-\dfrac{9}{10}}}\div 13\dfrac{1}{2}[4\dfrac{1}{2}\div \lbrace3-\left(2-\dfrac{1}{2}\right)\rbrace]\times 4\dfrac{1}{2}\) is ?

1. \(\dfrac{4}{3}\)
2. \(\dfrac{5}{9}\)
3. \(\dfrac{5}{6}\)
4. \(\dfrac{8}{3}\)

Answer 1

Correct Answer - Option 2 : \(\dfrac{5}{9}\)

Given:

\({\dfrac{1\dfrac{1}{4}\div1\dfrac{1}{2}}{\dfrac{1}{15}+1-\dfrac{9}{10}}}\div 13\dfrac{1}{2}[4\dfrac{1}{2}\div \lbrace3-\left(2-\dfrac{1}{2}\right)\rbrace]× 4\dfrac{1}{2}\)

Calculation:

\({\dfrac{\dfrac{5}{4}\div\dfrac{3}{2}}{\dfrac{16}{15}-\dfrac{9}{10}}}\div \dfrac{27}{2}[\dfrac{9}{2}\div \lbrace3-\left(\dfrac{3}{2}\right)\rbrace]× \dfrac{9}{2}\)

\({\dfrac{\dfrac{5}{6}}{\dfrac{1}{6}}}\div \dfrac{27}{2}[\dfrac{9}{2}\div \dfrac{3}{2}]× \dfrac{9}{2}\)

\(5\div \dfrac{27 \times3}{2}× \dfrac{9}{2}\)

\(5\times \dfrac{2}{27 \times3}× \dfrac{9}{2}\)

⇒ 5/9

∴ The required result will be 5/9.