Question

Arpit covered two-thirds of a journey in one day. The next day, he covered half of the remaining journey. What is the length of the whole journey, if he had covered 560 km in these two
days?​

Answer 1

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

$\:\:$

$\large\underline{\green{\bf Given :-}}$

$\:\:$

• Arpit covered two-thirds of a journey in one day

$\:\:$

• The next day, he covered half of the remaining journey

$\:\:$

• He had covered 560 km in these two days

$\:\:$

$\large\underline{\red{\bf To \: Find :-}}$

$\:\:$

• Length of the whole journey

$\:\:$

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

$\:\:$

• Let the length of the whole journey be "x"

$\:\:$

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

$\:\:$

Arpit covered two-thirds of a journey in one day

$\:\:$

$\underline{\bold{\texttt{Length covered in 1st day :}}}$

$\:\:$

➜ $\sf \dfrac { 2 } { 3 } × x$ ⚊⚊⚊⚊ ⓵

$\:\:$

$\underline{\bold{\texttt{Remaining length of journey :}}}$

$\:\:$

➜ $\sf x - \dfrac { 2x} { 3 }$

$\:\:$

➜ $\sf \dfrac { 3x - 2x } { 3 }$

$\:\:$

➜ $\sf \dfrac { x } { 3 }$

$\:\:$

Also given that the next day, he covered half of the remaining journey

$\:\:$

$\underline{\bold{\texttt{Length covered in 2nd day :}}}$

$\:\:$

➜ $\sf \dfrac { x } { 3 } × \dfrac { 1 } { 2 }$

$\:\:$

➜ $\sf \dfrac { x } { 6 }$ ⚊⚊⚊⚊ ⓶

$\:\:$

Given that he covered 560 km in these two days

$\:\:$

Thus,

$\:\:$

⟮ Equation ⓵ + ⓶ ⟯

$\:\:$

➜ $\sf \dfrac { 2x } { 3 } + \dfrac { x } { 6 } = 560$

$\:\:$

➜ $\sf \dfrac { 4x + x } { 6 } = 560$

$\:\:$

➜ $\sf \dfrac { \cancel 5x } { 6 } = \cancel { 560}$

$\:\:$

➜ $\sf \dfrac { x } { 6 } = 112$

$\:\:$

➜ x = 6 × 112

$\:\:$

➨ x = 672

$\:\:$

• Hence the length of his whole journey is 672 km

$\:\:$

═════════════════════════