Question

Nilu covers a distance by walking for 6 h,
while returning, his speed decreases by
2 km/h and he takes 9 h to cover the
same distance. What was her speed
while returning?
(a) 2 km/h
(b) 5 km/h
C) 4 km/h
(d) 7 km/h
(e) None of these​

Answer 1

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

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

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• Nilu covers a distance by walking for 6 h

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• While returning his speed decreases by 2 km/h

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• He took 9h to return covering the same distance

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

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• Speed while returning

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

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• Let the distance be "d"

• Let the original speed be "s"

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We know that ,

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➠ d = s × t ⚊⚊⚊⚊ ⓵

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Where,

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• d = Distance

• s = Speed

• t = Time taken

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

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Case 1 [ While Going ]

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Nilu covers a distance by walking for 6 h

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• d = d

• s = s

• t = 6

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⟮ Putting these values in ⓵ ⟯

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➜ d = s × t

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➜ d = s × 6 ⚊⚊⚊⚊ ⓶

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Case II [ While Returning ]

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Also given that , While returning his speed decreases by 2 km/h and he took 9h to return covering the same distance

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So,

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• d = d

• s = s - 2

• t = 9

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⟮ Putting these values in ⓵ ⟯

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➜ d = s × t ⚊⚊⚊⚊ ⓷

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➜ d = (s - 2) × 9 ⚊⚊⚊⚊ ⓷

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Equation ⓶ = Equation ⓷

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So,

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➜ s × 6 = (s - 2) × 9

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➜ 6s = 9s - 18

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➜ 9s - 6s = 18

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➜ 3s = 18

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➜ $\sf s = \dfrac { 18 } { 3 }$

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➨ s = 6 km/hr ⚊⚊⚊⚊ ⓸

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• Hence the original speed is 6 km/hr

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$\underline{\bold{\texttt{Speed while returning :}}}$

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Given that speed is decreased by 2

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So,

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➜ s - 2 ⚊⚊⚊⚊ ⓹

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⟮ Putting s = 6 from ⓸ to ⓹ ⟯

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➜ 6 - 2

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➨ 4 km/hr

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• Hence the speed while returning is 4 km/hr

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Thus option (c) is correct

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