Question

One third of a pole is painted red, one fifth is painted blue and the rest is painted white. If the portion which is painted white is 210cm long, what is the length of the pole?

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\:\:$

$\green{\underline \bold{Given :}}$

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• One third of the pole is painted red.

• One fifth of the pole is painted blue.

• Rest of the portion of pole is painted white.

• White portion is 210 cm long.

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$\red{\underline \bold{To \: Find:}}$

$\:\:$

• The length of pole.

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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Let the length of pole be 'x' cm

$\:\:$

$\underline{\bold{\texttt{Painted red:}}}$

$\:\:$

$\purple\longrightarrow$ $\sf \dfrac { 1 } { 3 } \times x$

$\:\:$

$\underline{\bold{\texttt{Painted blue:}}}$

$\:\:$

$\purple\longrightarrow$ $\sf \dfrac { 1 } { 5 } \times x$

$\:\:$

$\underline{\bold{\texttt{Length of pole painted red or blue :}}}$

$\:\:$

$\purple\longrightarrow$ $\sf \dfrac { 1 } { 3 } \times x + \dfrac { 1 } { 5 } \times x$

$\:\:$

$\sf \longmapsto \dfrac { 5x + 3x} { 15 }$

$\:\:$

$\bf \dashrightarrow \dfrac { 8x} { 15}$

$\:\:$

$\underline{\bold{\texttt{White portion of pole :}}}$

$\:\:$

$\sf \longmapsto x - \dfrac { 8x} { 15}$

$\:\:$

$\sf\longmapsto \dfrac { 15x - 8x } { 15 }$

$\:\:$

$\bf \dashrightarrow \dfrac { 7x } { 15 }$

$\:\:$

$\purple{\underline \bold{According \: to \: the \ question :}}$

$\:\:$

$\sf \implies \dfrac { 7x } { 15 } = 210$

$\:\:$

$\sf \longmapsto 7x = 3150$

$\:\:$

$\sf \longmapsto x = \dfrac { 3150 } { 7 }$

$\:\:$

$\bf \dashrightarrow x = 450 \: cm$

$\:\:$

Hence length of pole is 450 cm.

$\rule{200}5$