Question

2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.

Class 10
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Answer 1

Given that,

▶ 2 women and 5 men can together finish an embroidery work in 4 days. (1)

Also,

▶ 3 women and 6 men can finish it in 3 days. (2)

We have to find the time taken by a single woman alone to finish the work, also that taken by single man alone.

Let the work done by woman and man in a single day be x and y respectively.

(1) becomes,

⇒ 2/x + 5/y = 1/4 [ In a single day ] ...(3)

(2) becomes,

⇒ 3/x + 6/y = 1/3 [ In a single day ] ...(4)

Let, 1/x = a & 1/y = b

Eq.(3) becomes,

⇒ 2a + 5b = 1/4 ...(5)

Eq.(4) will be now,

⇒ 3a + 6b = 1/3 ...(6)

Multiply (5) by 3 and (6) by 2, To make the coefficient of a same.

⇒ 6a + 15b = 3/4 ...(7)

⇒ 6a + 12b = 2/3 ...(8)

Subtract (7) from (8), we get

⇒ 6a + 12b - 6a - 15b = 2/3 - 3/4

⇒ -3b = (8 - 9)/12

⇒ -3b = -1/12

⇒ b = 1/36

Substitute b = 1/36 in (6)

⇒ 3a + 6×1/36 = 1/3

⇒ 3a + 1/6 = 1/3

⇒ 3a = (2-1)/6

⇒ a = 1/18

Now, We assumed, a = 1/x & b = 1/y

Therefore, x = 18 & y = 36

Hence, A single woman alone will take 18 days to finish the work while a single man alone will take 36 days.

Answer 2

Answer:

$\underline{\bigstar\:\textsf{According to the given Question :}}$

$:\implies\sf (2W+5M) \times 4days=(3W+6M) \times 3days\\\\\\:\implies\sf (2W+5M) \times 4=(3W+6M) \times 3\\\\\\:\implies\sf 8W+20M = 9W+18M\\\\\\:\implies\sf 20M - 18M = 9W - 8W\\\\\\:\implies\sf 2M = W\\\\\\:\implies\sf \dfrac{M}{W} = \dfrac{1}{2}\\\\\\:\implies\sf M :W =1:2$

$\rule{200}{1}$

1 Woman can alone finish :

$\dashrightarrow\sf\:\: (2W+5M) \times 4days=1W \times Days\\\\\\\dashrightarrow\sf\:\:(2 \times2 + 5 \times 1) \times 4 = 1 \times 2 \times Days\\\\\\\dashrightarrow\sf\:\: (4 + 5) \times 4 = 2 \times Days\\\\\\\dashrightarrow\sf\:\: 9 \times 2 = Days\\\\\\\dashrightarrow\sf\:\: Days = 18$

⠀⠀⠀⠀⠀───────────────

1 Man can alone finish :

$\dashrightarrow\sf\:\: (2W+5M) \times 4days=1M \times Days\\\\\\\dashrightarrow\sf\:\:(2 \times2 + 5 \times 1) \times 4 = 1 \times 1 \times Days\\\\\\\dashrightarrow\sf\:\: (4 + 5) \times 4 = 1 \times Days\\\\\\\dashrightarrow\sf\:\: 9 \times 4 = Days\\\\\\\dashrightarrow\sf\:\: Days = 36$