8 men and 12 women can finish a piece of work | vedclass

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Question

(A) Let the time taken by one man to finish the work be $x$ days and by one woman be $y$ days.Work done by one man in $1$ day = $1/x$.Work done by one

Vedclass · Accepted Answer

Man: $140$ days,Woman: $280$ days

Vedclass · Answer

(A) Let the time taken by one man to finish the work be $x$ days and by one woman be $y$ days.Work done by one man in $1$ day = $1/x$.Work done by one woman in $1$ day = $1/y$.According to the problem:$10(8/x + 12/y) = 1 \implies 8/x + 12/y = 1/10$  (Equation $1$)$14(6/x + 8/y) = 1 \implies 6/x + 8/y = 1/14$  (Equation $2$)Let $u = 1/x$ and $v = 1/y$.$8u + 12v = 1/10 \implies 80u + 120v = 1$  (Equation $3$)$6u + 8v = 1/14 \implies 84u + 112v = 1$  (Equation $4$)Solving the system: From Equation $3$,$v = (1 - 80u)/120$. Substituting into Equation $4$:$84u + 112((1 - 80u)/120) = 1$$84u + (14/15)(1 - 80u) = 1$$1260u + 14 - 1120u = 15$$140u = 1 \implies u = 1/140$.So,$x = 140$ days.Substituting $u = 1/140$ into $80(1/140) + 120v = 1$:$4/7 + 120v = 1 \implies 120v = 3/7 \implies v = 1/280$.So,$y = 280$ days.Therefore,one man takes $140$ days and one woman takes $280$ days.

$8$ men and $12$ women can finish a piece of work in $10$ days. While $6$ men and $8$ women can finish it in $14$ days. Find the time taken by one man alone and that by one woman alone to finish the work.

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