Question

12 men or 15 women can do a piece of work in 21
days. Find the number of days required to complete
the same work by 6 men and 10 women.
(a) 15
(b) 18
(c) 21
(d) 24
(​

Answer 1

Answer:

6 men and 10 women can complete in 15 days  

Step-by-step explanation:

Answer 2

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

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$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

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• 12 men or 15 women can do a piece of work in 21 days

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$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

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• Number of days required to complete the same work by 6 men and 10 women

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$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

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Given that , 12 men or 15 women can do a piece of work in 21 days

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➜ i.e 12 men = 15 women

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⟮ Dividing above by 12 to get one man's work in term of women ⟯

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➜ $\sf 1 man = \dfrac { 15 } { 12 } \: women$

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➜ $\sf 1 man = \dfrac { 5 } { 4 } \: women$

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⟮ Multiplying above equation by 6 to get 6 men work in term of women ⟯

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➜ $\sf 6 men = \dfrac { 5 } { 4 } \times 6 \: women$

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➜ $\sf 6 men = \dfrac { 15} { 2 } \: women$ ⚊⚊⚊⚊ ⓵

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➜ 6 men + 10 women ⚊⚊⚊⚊ ⓶

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⟮ Putting the values of 6 men from ⓵ to ⓶ ⟯

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➜ 6 men + 10 women

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➜ $\sf \dfrac { 15} { 2 } \: women + 10 \: women$

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➜ $\sf \dfrac { 35 } { 2 } \: women$ ⚊⚊⚊⚊ ⓷

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Given that 15 women can finish the work in 21 days

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Clearly days and women are in inverse relation

i.e If the number of women are increased then the days required to finish the work will decrease

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• Let 1 women can finish the work in "x" days

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So,

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$\sf \underline { Women } \: \: \: \: \: \: \: \: \: \: \: \: \underline { Days }$

$\sf 15 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 21$

$\sf 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x$

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➜ 15 × 21 = x × 1

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➜ x = 315 ⚊⚊⚊⚊ ⓸

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• Hence 1 women can finish the work in 315 days

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From ⓷

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$\sf \dashrightarrow \footnotesize{ 6 \: men \: \& \: 10 \: women = \dfrac { 35 } { 2 } \: women }$ ⚊⚊⚊⚊ (z)

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Here also days and women are in inverse relation

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From ⓸ we got that 1 women can finish the work in 315 days

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• $\bf Let \: \dfrac { 35 } { 2 } \: women \: can \: finish \: the \: work \: in \: "y" \: days$

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So,

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$\sf \underline { Women } \: \: \: \: \: \: \: \: \: \: \: \: \underline { Days }$

$\sf \: \: 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 315$

$\sf \dfrac { 35 } { 2 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: y$

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➜ $\sf 1 \times 315 = \dfrac { 35 } { 2 } \times y$

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➜ $\sf y = \dfrac { 315 } { \dfrac { 35 } { 2 } }$

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➜ $\sf y = \dfrac { 315 } { 1 } \times \dfrac { 2 } { 35 }$

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➜ y = 9 × 2

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➨ y = 18

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$\bf Hence \: \dfrac { 35 } { 2 } \: women \: can \: finish \: the \: work \: in \: 18 \: days$

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$\bf { From \: equation \: (z) \: we \: got \: that \: 6 \: men \: and \: 10 \: women \: = \: \dfrac { 35 } { 2 } \: women }$

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Thus ,

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• Hence 6 men and 10 women can finish the work in 18 days

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∴ Option (b) 18 is correct