Given: Time taken by X to complete the work = 8 days Time taken by Y to complete the work = 12 days Total amount = Rs. 9000 Concept used: Efficiency = 1/Time Calculations: In building the wall, X and Y worked for 4 days each, while Z worked for only 2 days Work done by X in 1 day = 1/8 Work done by Y in 1 day = 1/12 ⇒ Work done by X and Y together in 4 days = 4 × (1/8 + 1/12) = 4 × 5/24 = 5/6 ⇒ Work done by Z in 2 days = 1 – 5/6 = 1/6 ∵ Total money paid = Rs. 9000 ∴ Money received by Z = 1/6 × 9000 = Rs. 1500 [ alt="Alternate Method Sunny 28.7.21" src="//storage.googleapis.com/tb-img/production/21/07/Alternate%20Method_Sunny_28.7.21.png" style="width: 241px; height: 51px;"> Concept used: Divide the sum of money according to the work done by the person. Efficiency = (Total work)/(Total time) Calculations: Total work = LCM of (8 and 12 days) = 24 unit Efficiency of X = 24/8 = 3 units Efficiency of Y = 24/12 = 2 units Total work done by X and Y in one day = 3 + 2 = 5 unit Total work done by X and Y in 2 days = 5 × 2 = 10 unit Remaining work = 24 - 10 = 14 units According to question The remaining work will be completed by X and Y with the help of Z in 2 days So, Efficiency of (X + Y + Z) = 14/2 = 7 The efficiency of Z = 7 - Efficiency of (X and Y) ⇒ Efficiency of Z = 7 - 5 = 2 Total work done by Z in last two days = 2 × 2 = 4 units Amount received by Z = (9000/24) × 4 = Rs. 1500 ∴ Amount received by Z is Rs. 1500