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In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option.
Quantity A: 8 men working 9 hours a day can complete 2 units of work in 20 days. In how many days can 6 men working 10 hours a day to complete 3 unit of work?
Quantity B: P is 70% more efficient than Q, while R is 45% less efficient that Q. If P and R can together do a certain work in 16 days, in how many days will Q do the same work alone?
  • a)
    Quantity A ≤ Quantity B
  • b)
    Quantity A ≥ Quantity B
  • c)
    Quantity A < Quantity B
  • d)
    Quantity A > Quantity B
  • e)
    Quantity A = Quantity B or No relation
Correct answer is option 'E'. Can you explain this answer?
Verified Answer
In the following question, two statements are numbered as A and B. On ...
Quantity A:
[M1 × T1 × D1]/W1 = [M2 × T2 × D2]/W2
= [8 × 9 × 20]/2 = [6 × 10 × D2]/3
= D2 = [8 × 9 × 10]/[2 × 10]
D2 = 36 days
Quantity B:
Let Q take ‘x’ day to do the work alone
= Q’s 1 day work = 1/x
As, P is 70% more efficient than Q
= P’s 1 day work = (100 + 70)% of Q’s 1 day work = (17/10) × (1/x) = 17/10x
Similarly, R is 45% less efficient than Q
= R‘s 1 day work = (100 – 45)% of Q’s 1 day work = (55/100) × (1/x) = 11/20x
Now, P and R can together do the work in 16 days
= (P & R)’s 1 day work = 1/16
= (17/10x) + (11/20x) = 1/16
= 9/4x = 1/16
= x = 16 × (9/4) = 36 days
= Q can do the work alone in 36 days
= Quantity A = Quantity B
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Most Upvoted Answer
In the following question, two statements are numbered as A and B. On ...
Quantity A:
[M1 × T1 × D1]/W1 = [M2 × T2 × D2]/W2
= [8 × 9 × 20]/2 = [6 × 10 × D2]/3
= D2 = [8 × 9 × 10]/[2 × 10]
D2 = 36 days
Quantity B:
Let Q take ‘x’ day to do the work alone
= Q’s 1 day work = 1/x
As, P is 70% more efficient than Q
= P’s 1 day work = (100 + 70)% of Q’s 1 day work = (17/10) × (1/x) = 17/10x
Similarly, R is 45% less efficient than Q
= R‘s 1 day work = (100 – 45)% of Q’s 1 day work = (55/100) × (1/x) = 11/20x
Now, P and R can together do the work in 16 days
= (P & R)’s 1 day work = 1/16
= (17/10x) + (11/20x) = 1/16
= 9/4x = 1/16
= x = 16 × (9/4) = 36 days
= Q can do the work alone in 36 days
= Quantity A = Quantity B
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In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option.Quantity A: 8 men working 9 hours a day can complete 2 units of work in 20 days. In how many days can 6 men working 10 hours a day to complete 3 unit of work?Quantity B: P is 70% more efficient than Q, while R is 45% less efficient that Q. If P and R can together do a certain work in 16 days, in how many days will Q do the same work alone?a)Quantity A ≤ Quantity Bb)Quantity A ≥ Quantity Bc)Quantity A < Quantity Bd)Quantity A > Quantity Be)Quantity A = Quantity B or No relationCorrect answer is option 'E'. Can you explain this answer?
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