X can complete 14 of a work in 3 days and Y can complete 16 of the same ​ ​ work in 4 days. X and Y worked together for 6 days and Z alone completed the remaining work in 8 days. If Y and Z work together, how much time will they take to complete the same work?

Explanation

Given: X can complete 14 of a work in 3 days ​ Y can complete 1 of the same work in 4 days. 6 ​ Calculation: X can complete 1 of a work in 3 days 4 ​ So, X can complete the total work in 3 × 4 = 12 days Similarly, Y can complete 1 of the same work in 4 days. 6 ​ So, Y can completer the total work in 4 × 6 = 24 days LCM of 12 and 24 is 24 i.e total work So, efficiency of X = 24/12 = 2 units/day Efficiency of Y = 24/24 = 1 unit/day In 6 days they will complete = 6 × 3 ⇒ 18 units Remaining = 24 - 18 ⇒ 6 units will be completed by Z in 8 days So, the efficiency of Z = 6/8 or 3/4 Now, Effective efficiency of Y and Z = 1 + 3/4 ⇒ 7/4 Time = ⇒ 24 × 47 ⇒ 96 7 ​ 24 7 4 ​ ​ ​ or 13 57 days ​ ∴ They will take 13 57 days to complete the same work. ​