Question

13. The work done by (x - 2) men in (4x + 1) days
and the work done by (4x + 1) men in
(2x - 3) days are in the ratio 3: 8. Find the
value of x.​

Answer 1

Given :-

work done by (x - 2) men in (4x + 1) days : work done by (4x + 1) men in (2x - 3) days = 3: 8.

To Find :-

• Value of x ?

Concept Used :-

• The number of people working is directly proportional to the amount of work done.
• The number of days worked is directly proportional to the amount of work done.
• The number of people working is inversely proportional to the number of days worked.

Solution :-

From Above Told Concept we can say That,

☛ (M₁ * D₁)/ W₁ = (M₂ * D₂) / W₂

☛ (M₁ * D₁) / (M₂ * D₂) = W₁ / W₂

Given That :-

☞ M₁ = (x - 2)

☞ D₁ = (4x + 1)

☞ M₂ = (4x + 1)

☞ D₂ = (2x - 3)

☞ W₁ = 3

☞ W₂ = 8

Putting All values Now, we get :-

⟼ [(x - 2)(4x + 1)] / [(4x + 1)(2x - 3)] = 3/8

Cross - Multiply,

⟼ 8[(x - 2)(4x + 1)] = 3 [(4x + 1)(2x - 3)]

⟼ 8(4x² + x - 8x - 2) = 3(8x² - 12x + 2x - 3)

⟼ 8(4x² - 7x - 2) = 3(8x² - 10x - 3)

⟼ 32x² - 56x - 16 = 24x² - 30x - 9

⟼ 32x² - 24x² - 56x + 30x - 16 + 9 = 0

⟼ 8x² - 26x - 7 = 0

⟼ 8x² - 28x + 2x - 7 = 0

⟼ 4x(2x - 7) + 1(2x - 7) = 0

⟼ (2x - 7)(4x + 1) = 0

⟼ 2x - 7 = 0

⟼ 2x = 7

⟼ x = (7/2)

Or,

⟼ 4x + 1 = 0

⟼ 4x = (-1)

⟼ x = (-1)/4 . ( - ve ≠ ).

Hence, Value of x will be (7/2) .

Answer 2

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$\huge\tt{GIVEN:}$

• The work done by (x - 2) men in (4x + 1) days and the work done by (4x + 1) men in (2x - 3) days are in the ratio 3: 8.

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$\huge\tt{TO~FIND:}$

• value of x.

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$\huge\tt{SOLUTION:}$

We are assuming that each person does the same amount of work...

We can say that,

man = 1 units,

↪Amount of work done by (x − 2) men in (4x + 1) days = Amount of work done by (x − 2)(4x + 1) men in one day = (x − 2)(4x + 1) units of work

Similarly,

↪Amount of work done by (4x + 1) men in (2x − 3) days = (4x + 1)(2x − 3) units of work

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According to the question,

➡(x-2)(4x+1)/(4x+1)(2x-3)=3/8

➡(x-2/2x-3)= 3/8

➡8x-16= 6x-9

➡2x=7

➡x= 7/2

➡x=3.5

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