1.

X,Y and Z are partners sharingprofits in theraito of 5 :3:2. Calculate new profit -sharing ratio, sacrificing ratio, gaining ratioin eachof the followingcases: Case 1. If Zacquires1//5thshare from X. Case 2.If Z acquires 1//5th share equallyfrom X and Y. Case 3.If X,Y and Z decide to share equallyform X and Y. Case 4. IfZ acquire 1//5th share of Xand 1//6th Share of Y.

Answer»

Solution :Case.1
(A) Their existingshare
(B) Share ACQUIRED by Z and X TheirNew Share (A+B)

Thus, New Profits-sharing Ratio of X ,Y and Z `= (3)/(10): (3)/(10) : (4)/(10) = 3: 3:4,` Sacrifice of `X = 1//5, ` Gainof `Z = 1//5`
Case 2.
(A) Theirexisting share
(B). Share acquired by Z form X and Y
Their New Share (A + B)

Thus, New Profit- SharingRatio of X,Y andZ `= (4)/(10): (2)/(10): (4)/(10) = 2:1:2,`
Sarcrifing RatiobetweenX and Y`= 1//10 : 1/10 = 1:1,` Gain ofZ`= 2//10`
Case 3.Sacrificing /(Gaining) Share = Old Share - New Share
`{:(,,("X"),("Y"),("Z")),(("A") ,"Their existing(old)share",5//10,3//10,2//10),(("B"), "Their new share",1//3,1//3,1//3):}`
`X = (5)/(10)- (1)/(3) = (15-10)/(30) =(5)/(30)("Sacrifice")`
`Y = (3)/(10) - (1)/(3) = (9-1)/(30) = (1)/(30)`(beingnegative result, it is a gain)
`Z = (2)/(10) - (1)/(3) =(6-10)/(30) = - (4)/(30)`(being negativeresult, it is a gain.)
Thus, Y GAINS `1//30th` share Zgain by `4//30th` (Share of Yand Z haveincreased) and X scarifices by `5//30th` share. Gaining Ratio betweenY and Z `= (1)/(30) : (4)/(30) =1:4`
Case. 4
`{:(,,("X"),("Y"),("Z")),((A),"Their existing(old)share",5//10,3//10,2//10),((B), "Share acquired by Z from",,,):}`
` X = (5)/(10) xx (1)/(5) xx (1)/(10), Y = (3)/(10) xx (10)/(6) = (1)/(20)`
(C) Total share acquired by `Z = (1)/(10)+ (1)/(20) =(3)/(20)`
Calculationof NewProfit-sharingRatio and Sacrifing Ratio :

Thus, New Profit-SharingRatio of X,Y and Z `= (8)/(20):(5)/(20) : (7)/(20) = 8 :5:7` Gainof `Z = (3)/(20),` SacrficingbetweenX and Y= 2 : 1.


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