Question

A and B can together colour a counting in 20 minutes &
alone can tolour the painting in 25 minutes in how much
time con B alone colour
Balone colour in the painting?​

Answer 1

A n s w e r

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G i v e n

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• A and B can together colour a painting in 20 minutes

• A alone can finish the painting in 25 minutes

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F i n d

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• Time in which B alone can finish the painting

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S o l u t i o n

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• Let B can finish the painting in 'z' minutes

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$\underline{ \underline{\bold{\texttt{One minute work of A :}}}}$

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Given that A can finish the painting in 25 minutes

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: ➜ $\sf \dfrac { 1 } { 25 }$

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$\underline{ \underline{\bold{\texttt{One minute work of B :}}}}$

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We assumed B to finish the painting in 'z' minutes

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: ➜ $\sf \dfrac { 1 } { z}$

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$\underline{ \underline{\bold{\texttt{1 minute work of A \& B together :}}}}$

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: ➜ $\sf \dfrac { 1 } { 25 } + \dfrac { 1 } { z }$

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$\underline{ \underline{\bold{\texttt{20 minutes work of A \& B together :}}}}$

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: ➜ $\sf 20\bigg(\dfrac { 1 } { 25 } + \dfrac { 1 } { z }\bigg)$

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It is given that working together for 20 minutes A & B can finish the painting

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Thus ,

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: ➜ $\sf 20\bigg(\dfrac { 1 } { 25 } + \dfrac { 1 } { z }\bigg) = 1$

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: ➜ $\sf 20\bigg(\dfrac { z + 25} { 25z } \bigg) = 1$

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: ➜ $\sf 4\bigg(\dfrac { z + 25} { 5z} \bigg) = 1$

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: ➜ 4(z + 25) = 5z

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: ➜ 4z + 100 = 5z

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: ➜ 5z - 4z = 100

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: : ➨ z = 100

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• Hence B can finish the painting in 100 minutes

Answer 2

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G i v e n :-

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A and B can together colour a painting in 20 minutes

A alone can finish the painting in 25 minutes

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F i n d :-

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Time in which B alone can finish the painting

$\:\:$

S o l u t i o n :-

$\:\:$

Let B can finish the painting in 'z' minutes

$\:\:$

$\underline{ \underline{\bold{\texttt{One minute work of A :}}}}$

$\:\:$

Given that A can finish the painting in 25 minutes

$\:\:$

: ➜ $\sf \dfrac { 1 } { 25 }$

$\:\:$

$\underline{ \underline{\bold{\texttt{One minute work of B :}}}}$

$\:\:$

We assumed B to finish the painting in 'z' minutes

$\:\:$

: ➜ $\sf \dfrac { 1 } { z}$

$\:\:$

$\underline{ \underline{\bold{\texttt{1 minute work of A \& B together :}}}}$

$\:\:$

: ➜ $\sf \dfrac { 1 } { 25 } + \dfrac { 1 } { z }$

$\:\:$

$\underline{ \underline{\bold{\texttt{20 minutes work of A \& B together :}}}}$

$\:\:$

: ➜ $\sf 20\bigg(\dfrac { 1 } { 25 } + \dfrac { 1 } { z }\bigg)$

$\:\:$

• It is given that working together for 20 minutes A & B can finish the painting

$\:\:$

Thus ,

$\:\:$

: ➜ $\sf 20\bigg(\dfrac { 1 } { 25 } + \dfrac { 1 } { z }\bigg) = 1$

$\:\:$

: ➜ $\sf 20\bigg(\dfrac { z + 25} { 25z } \bigg) = 1$

$\:\:$

: ➜ $\sf 4\bigg(\dfrac { z + 25} { 5z} \bigg) = 1$

$\:\:$

: ➜ 4(z + 25) = 5z

$\:\:$

: ➜ 4z + 100 = 5z

$\:\:$

: ➜ 5z - 4z = 100

$\:\:$

: : ➨ z = 100

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• Hence B can finish the painting in 100 minutes