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? Correct Answer Quantity A = Quantity B or No relation Quantity A: /W1 = /W2 ⇒ /2 = /3 ⇒ D2 = / 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