Question

Q) ¼ part of a rod is in mud, its half is in water and 0.75 m is above the water. Find the length of the rod ?​

Answer 1

$\huge \underline{ \tt{Answer \: : }}$

• 3 metre.

$\huge{ \underline{ \tt{Given\: : }}}$

• the portion of the of the rod .

$\huge{ \underline{ \tt{To \ find\: : }}}$

• the length of the rod ?

$\huge{ \underline{ \tt{ Using\: : }}}$

• the application of first degree equation in one variable.

$\huge{ \underline{ \tt{Information \: : }}}$

• $\tt let \: \: the \: \: lenth \: \: of \: \: the \: \: rod \: \: be \: \: {\bf{x}} \: metre \\ \\ \tt portion \: \: in \: \: mud \: = \: \frac{x}{4} \: m \\ \tt portion \: \: in \: \: water \: = \: \frac{x}{2} \: m \\ \tt portion \: \: above \: \: water \: = \: 0.75 \: m \\ \tt = \frac{75}{100} \: \: metre \\ \tt = {\frac{3}{4} \: \: metre }$

$\large{ \underline{ \bold{ \tt{Making \: equation \: form: }}}}$

• $\large \tt \red{ \ \frac{x}{4} + \frac{x}{2} + \frac{3}{4} = x}$

$\huge{ \underline{ \tt{Solution \: : }}}$

• $\tt { \ \frac{x}{4} + \frac{x}{2} + \frac{3}{4} = x} \\ \\ \tt \implies{ \ \frac{x}{4} + \frac{x}{2} - x = - \frac{3}{4} } \\ \tt \implies{ \ \frac{x + 2x - 4x} {4} = - \frac{3}{4} } \\ \tt \implies{ \ \frac{ - x} {4} = - \frac{3}{4} } \\ \tt \implies{ \ \frac{ - x} {4} \times ( - 4) = - \frac{3}{4} \times ( - 4)} \\ \large \green{ \tt{ \implies{x = 3}}}$

$\tt\pink{Length \: of \: the \: rod \: = } \huge\boxed{\purple{\rm{3 \: m}}}$