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Mathematics

3 men and 4 boys can do a piece of work in 14 days, while 4 men and 6 boys can do it in 10 days. How long would it take 1 boy to finish the work ?

Linear Equations

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Answer

Let one man's one day work be x and one boy's one day work be y.

3 men and 4 boys complete the work in 14 days.

⇒ 3x + 4y = 114\dfrac{1}{14} ……………….(1)

4 men and 6 boys complete the work in 10 days.

⇒ 4x + 6y = 110\dfrac{1}{10} ……………….(2)

Multiply equation (1) by 4 and equation (2) by 3,

(3x + 4y = 114\dfrac{1}{14}) x 4

⇒ 12x + 16y = 27\dfrac{2}{7} …………………(3)

(4x + 6y = 110\dfrac{1}{10}) x 3

⇒ 12x + 18y = 310\dfrac{3}{10} …………………..(4)

Subtracting equation (3) from equation (4), we get:

12x+16y=2712x+18y=310−−−−2y=27−310−2y=2070−2170−2y=−170y=1140\begin{matrix} & 12x & + & 16y & = & \dfrac{2}{7} \ & 12x & + & 18y & = & \dfrac{3}{10} \ & - & &- & & - \ \hline & & & -2y & = & \dfrac{2}{7} - \dfrac{3}{10} \ & & & -2y & = & \dfrac{20}{70} - \dfrac{21}{70} \ & & & -2y & = & - \dfrac{1}{70} \ & & & y & = & \dfrac{1}{140} \ \end{matrix}

⇒ y = 1140\dfrac{1}{140}

Hence, one boy can complete the whole work in 140 days.

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