It was intended that Rs.19.50 should be divided between A,B&C in the ratio 2:3:4 but by mistake distribution was made in the ratio 1/2:1/3:1/4.how much does each gain or loss by this error?
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Amount = 19.50
Wrongly distributed ratio:
A : B : C = 1/2 : 1/3 : 1/4 = 6/12 : 4/12 : 3/12 = 6:4:3
13 parts = 19.50
1 part = 1.5
A-- 6 parts = 6*1.5 = 9
B-- 4 parts = 4*1.5 = 6
C-- 3 parts = 3*1.5 = 4.5
............................................................................................
Actual intended ratio:
A:B:C = 2:3:4
9 parts == 19.5
1 part == 19.5/9 = 6.5/3
A-- 2 parts = 2*6.5/3 = 13/3
B-- 3 parts = 3*6.5/3 = 6.5
C-- 4 parts = 4*6.5/3 = 26/3
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Gain or Loss due to 'error'
A had a gain of: 9 - 13/3 = 14/3 or 4.67 Rs.
B had a loss of: 6.5 - 6 = 0.5 Rs.
C had a loss of 26/3 - 4.5 = 12.5/3 or 4.167 Rs.
Hope it helps.
Wrongly distributed ratio:
A : B : C = 1/2 : 1/3 : 1/4 = 6/12 : 4/12 : 3/12 = 6:4:3
13 parts = 19.50
1 part = 1.5
A-- 6 parts = 6*1.5 = 9
B-- 4 parts = 4*1.5 = 6
C-- 3 parts = 3*1.5 = 4.5
............................................................................................
Actual intended ratio:
A:B:C = 2:3:4
9 parts == 19.5
1 part == 19.5/9 = 6.5/3
A-- 2 parts = 2*6.5/3 = 13/3
B-- 3 parts = 3*6.5/3 = 6.5
C-- 4 parts = 4*6.5/3 = 26/3
---------------------------------------------------------------------------
Gain or Loss due to 'error'
A had a gain of: 9 - 13/3 = 14/3 or 4.67 Rs.
B had a loss of: 6.5 - 6 = 0.5 Rs.
C had a loss of 26/3 - 4.5 = 12.5/3 or 4.167 Rs.
Hope it helps.
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0
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