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Fiver men and 2 women can do a piece of ...

Fiver men and 2 women can do a piece of work in 9 days , whereas 11 men and 5 women can do the same work in 4 days. To complete the same work in 6 days, the number of women required is :

A

20

B

18

C

15

D

16

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, let's break it down: ### Step 1: Understand the Work Done by Men and Women We know from the problem that: - 5 men and 2 women can complete the work in 9 days. - 11 men and 5 women can complete the same work in 4 days. ### Step 2: Calculate the Total Work Let's denote the work done by one man in one day as \( m \) and the work done by one woman in one day as \( w \). From the first scenario: - Work done by 5 men and 2 women in 1 day = \( 5m + 2w \) - Total work done in 9 days = \( 9(5m + 2w) \) From the second scenario: - Work done by 11 men and 5 women in 1 day = \( 11m + 5w \) - Total work done in 4 days = \( 4(11m + 5w) \) Since both expressions represent the same total work, we can set them equal to each other: \[ 9(5m + 2w) = 4(11m + 5w) \] ### Step 3: Expand and Rearrange the Equation Expanding both sides gives: \[ 45m + 18w = 44m + 20w \] Now, rearranging the equation: \[ 45m - 44m = 20w - 18w \] \[ m = 2w \] ### Step 4: Find the Ratio of Men to Women From the equation \( m = 2w \), we can express the ratio of men to women: \[ \frac{m}{w} = 2 \implies \text{Ratio of men to women} = 2:1 \] ### Step 5: Calculate Total Work Now, we can calculate the total work using either scenario. Let's use the first scenario: \[ \text{Total Work} = 9(5m + 2w) \] Substituting \( m = 2w \): \[ = 9(5(2w) + 2w) = 9(10w + 2w) = 9(12w) = 108w \] ### Step 6: Determine the Number of Women Required to Complete the Work in 6 Days We need to find out how many women are required to complete the total work (108w) in 6 days. Let \( x \) be the number of women required. The work done by \( x \) women in 6 days is: \[ 6(xw) = 6xw \] Setting this equal to the total work: \[ 6xw = 108w \] ### Step 7: Solve for \( x \) Dividing both sides by \( w \) (assuming \( w \neq 0 \)): \[ 6x = 108 \] \[ x = \frac{108}{6} = 18 \] ### Conclusion The number of women required to complete the work in 6 days is **18**. ---
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