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Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers. Quantity A : 10 men and 15 women can complete a piece of work in 15 days while 5men and 10 women can complete the work in 25 days. What part of work a woman can complete in 1 day? Quantity B : 5 women and 10 girls can complete stitching work in 10 days and 7 women and 5 girls can complete this same work in 15 days. What fraction of work remains if 6 girls work alone for 6 days?

Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers. Quantity A : 10 men and 15 women can complete a piece of work in 15 days while 5men and 10 women can complete the work in 25 days. What part of work a woman can complete in 1 day? Quantity B : 5 women and 10 girls can complete stitching work in 10 days and 7 women and 5 girls can complete this same work in 15 days. What fraction of work remains if 6 girls work alone for 6 days? Correct Answer Quantity A < Quantity B

Quantity A:

Let 1 men’s 1 day’s work = x and 1 women’s 1 day’s work = y

Then,

10x + 15y = 1/15

5x + 10y = 1/25

Solving above equation,

10x + 20y = 2/25

10x + 15y = 1/15

5y = (2/25) – (1/15)

5y = 5/375

y = 1/375

1 women’s 1 day’s work = 1/375

Fraction of work completed in 1 day by a women = 1/375

Quantity B:

Let 1 women’s 1 day’s work = a and 1 girl’s 1 day’s work = b

Given,

5a + 10b = 1/10

7a + 5b = (1/15)

Solving above equation,

35a + 70b = 7/10

35a + 25b = 5/15 = 1/3

Then,

45b = 7/10 – 1/3

45b = 11/30

b = 11/1350

1 girl’s 1 day’s work = 11/1350

6 girls 1 day’s work = 6 × 11/1350 = 11/225

6 girls 6 days work = 6 × 11/225 = 22/75

Remaining work after 6 days =

 = 1 – (22/75)

 = 53/75

From above solution,

Relation between Quantity A < Quantity B is established.

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